JEE Exam  >  JEE Notes  >  Mathematics (Maths) Class 12  >  NCERT Solutions: Exercise - 10.3 - Vector Algebra

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE PDF Download

Question 1: Find the angle between two vectors  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE and vector Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE with magnitudes √3  and 2, respectively having Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER:
Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 2: Find the angle between the vectorsExercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER : - The given vectors are .

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 3: Find the projection of the vector Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE on the vector Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE.

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

 

Question 4: Find the projection of the vector Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE  on the vector  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE.

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

 

Question 5: Show that each of the given three vectors is a unit vector

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

 

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Question 6:  Find Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE, if Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE
ANSWER:
Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


 Question 7: Evaluate the product Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER  

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 8: Find the magnitude of two vectors a and b, having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 9: Find Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE, if for a unit Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER:
Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 10: Show that  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE is perpendicular to  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE  ,for any two nonzero vectors a and b.

ANSWER : -

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 11: If , then what can be concluded about the vector ?

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 12:If Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE are unit vectors such that Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE, find the value of  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER:
Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


 Question 13: If either vector a = 0, then b = 0. But the converse need not be true. Justify your answer with an example.

ANSWER : -

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 14:

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

ANSWER : - The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


Question 15: Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.

ANSWER : - The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

 

Question 16: Show that the vectors 2i - j k, i - 3j - 5k and 3i - 4j - 4k  form the vertices of a right angled triangle.

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE


 Question 17: Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE is unit vector if

(A) λ = 1

(B) λ = –1     

(c) a = | λ|

(d) a = 1/| λ|

ANSWER :  Vector Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE is a unit vector if  Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE

The document Exercise - 10.3 - Vector Algebra NCERT Solutions | Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.
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FAQs on Exercise - 10.3 - Vector Algebra NCERT Solutions - Mathematics (Maths) Class 12 - JEE

1. What is vector algebra?
Ans. Vector algebra is a branch of mathematics that deals with the operations and properties of vectors. It involves the addition, subtraction, multiplication, and division of vectors, as well as finding their magnitude, direction, and components.
2. How are vectors represented in vector algebra?
Ans. Vectors in vector algebra are typically represented using a combination of magnitude and direction. They can be represented as arrows, with the length of the arrow representing the magnitude of the vector and the direction of the arrow indicating its direction.
3. What are the basic operations in vector algebra?
Ans. The basic operations in vector algebra include vector addition, vector subtraction, scalar multiplication, and dot product. Vector addition involves adding the corresponding components of two vectors. Vector subtraction is similar, but with the components subtracted. Scalar multiplication involves multiplying a vector by a scalar (a real number). The dot product is a way to find the angle between two vectors.
4. How do you find the magnitude of a vector in vector algebra?
Ans. The magnitude of a vector can be found using the Pythagorean theorem. If a vector has components (x, y, z), the magnitude can be calculated as √(x^2 + y^2 + z^2). This gives the length or size of the vector.
5. What is the significance of vector algebra in real-life applications?
Ans. Vector algebra has various real-life applications, such as in physics, engineering, and computer graphics. It is used to represent and manipulate forces, velocities, and displacements. It helps in solving problems related to motion, electrical circuits, fluid dynamics, and much more. Vector algebra plays a crucial role in understanding and analyzing physical phenomena and designing practical solutions.
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