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Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE PDF Download

Q. 1. Let Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE be vectors of length 3, 4, 5 respectively. Let Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE be perpendicular to  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE Then the length of vector  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE               (1981 - 2 Marks)

Ans. 5√2

Solution. 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Adding (1), (2) and (3) we get

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

= 50  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 2. The unit vector perpendicular to the plane determined by P(1, –1, 2), Q (2, 0, –1) and R(0, 2, 1) is .......          (1983 - 1 Mark)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. Required unit vector,  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 3. The area of the triangle whose vertices are A (1, –1, 2), B (2, 1, –1), C( 3, – 1, 2) is .......            (1983 - 1 Mark)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution.

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Q. 4. A, B, C and D, are four points in a plane with position vectors a, b, c and d respectively such that

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

The point D,  then, is the ................... of the triangle ABC.                 (1984 - 2 Marks)

Ans. orthocen tre

Solution. Given that Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEEare position vectors of points A, B, C and D respectively, such tha

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Clearly D is orthocentre of DΔABC


Q. 5.  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and the vectors  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEEFill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are non -coplanar, then the product abc = .......              (1985 - 2 Marks)

Ans. –1

Solution. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Operating  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE in first determinant

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Also given that the vectors  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are noncoplanar 

i.e.,  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

∴ We must have 1 + abc = 0 ⇒ abc = – 1


Q. 6. If  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are three non-coplanar vectors, then –  

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE               (1985 - 2 Marks)

Ans. 0

Solution. As given that  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are three noncoplan ar vectors,  therefore,  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Also by the property of scalar triple product we have

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 7. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are given vectors, then a vector B satisfying the equations  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE         (1985 - 2 Marks)

Ans.  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution.  

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Using equations (1) and (2) we get

1 + z + z + z = 3

⇒ z = 2/3 ⇒ y = 2/3, x =5/3

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 8. If the vectors  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE (a ≠ b ≠ c ≠ 1) are coplanar, then the value of Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEEFill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE                (1987 - 2 Marks)

Ans. 1

Solution. Given that the vectors  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE where a ≠ b ≠ c ≠ 1 are coplanar

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Taking (1 – a), (1 – b), (1 – c) common from R1, R2 and R3 respectively.

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

But a ≠ b ≠ c ≠ 1 (given)

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 9. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE respectively,, are given by ........                  (1987 - 2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE   ...(1)

Now, let  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE be the required vectors.

Then as per question 

Projection of  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

⇒  4x + 3y = 5            ..(2)

Also, projection of  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

⇒ 3λx – 4λy = 10λ
⇒  3x – 4y = 10              ...(3)

Solving (2) and (3), we get x = 2, y = – 1

∴ The required vector is  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 10. The components of a vector  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE along and perpendicular to a non-zero vector  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE ..........and .......respectively..              (1988 - 2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution.  Component of  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Component of  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 11. Given that Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE               (1991 -  2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Using equations (1) and (2) we get

1 + z + z + z = 3

⇒ z = 2/3 ⇒ y = 2/3, x =5/3

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 12. A unit vector coplanar with Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and perpendicular to  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE                  (1992 -  2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. Let  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE be a unit vector, coplanar with  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and also perpendicular to  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solving the above by cross multiplication method, we get 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

As Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE is a unit vector, therefore 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

∴ The required vector is  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Q. 13. A unit vector perpendicular to the plane determined by the points P(1, – 1, 2) Q(2, 0, –1) and R(0, 2, 1) is .......                   (1994 -  2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. We have position vectors of points  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Now any vector perpendicular to the plane formed by pts

PQR is given by Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

∴ Unit vector normal to plane  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Q. 14. A nonzero vector Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE is parallel to the line of intersection of the plane determined by the vectors Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and the plane determined by the vectors  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE The angle between Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and the vector Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE               (1996 - 2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. Eqn of plane containing vectors Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Similarly, eqn of plane containing vectors Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

⇒ (x – 1) (–1 – 0) – (y + 1) (1 – 0) + z (0 + 1) = 0
⇒ – x + 1 – y – 1 + z = 0
⇒ x + y – z = 0                    ....(2)

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE
Since Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE parallel to (1) and (2) 

a3 = 0 and a1 + a2 – a3 = 0 ⇒ a1 = – a2 , a3 = 0

∴ a vector in direction of  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Now  if θ is the angle between  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE then 

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE


Q. 15. If  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE are any two non-collinear unit vectors and  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE any vector, then  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE               (1996 - 2 Marks)

Ans. Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Solution. Let us consider Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Q. 16. Let OA = a, OB = 10 a + 2b and OC = b where O, A and C are non-collinear points. Let p denote the area of the quadrilateral OABC, and let q denote the area of the parallelogram with OA and OC as adjacent sides. If p = kq, then k = .......              (1997 - 2 Marks)

Ans. 6

Solution. q = area of parallelogram with  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

adjacent sides  Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

and p = area of quadrilateral OABC

Fill in the Blanks: Vector Algebra and Three Dimensional Geometry | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

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FAQs on Fill in the Blanks: Vector Algebra and Three Dimensional Geometry - JEE Advanced - 35 Years Chapter wise Previous Year Solved Papers for JEE

1. What are the basic operations in vector algebra?
Ans. The basic operations in vector algebra include addition, subtraction, scalar multiplication, dot product, and cross product.
2. How do you find the magnitude of a vector?
Ans. To find the magnitude of a vector, we use the formula: magnitude = √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector in three-dimensional space.
3. What is the significance of the dot product of two vectors?
Ans. The dot product of two vectors has several significances. It gives us information about the angle between the vectors, allows us to calculate the projection of one vector onto another, and helps in determining whether the vectors are perpendicular or parallel.
4. How is the cross product of two vectors calculated?
Ans. The cross product of two vectors is calculated using the determinant of a 3x3 matrix. The result is a vector perpendicular to both the given vectors and its magnitude is equal to the product of the magnitudes of the original vectors multiplied by the sine of the angle between them.
5. How is three-dimensional geometry related to vector algebra?
Ans. Three-dimensional geometry is closely related to vector algebra as vectors are used to represent points, lines, and planes in three-dimensional space. Vector operations such as dot product and cross product are used to solve geometric problems and determine the relationships between different geometric elements.
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