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   and vector  with magnitudes √3  and 2, respectively having

Question 2: Find the angle between the vectors

ANSWER : - The given vectors are .

Question 3: Find the projection of the vector  on the vector .

Question 4: Find the projection of the vector   on the vector  .

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

Question 6:  Find , if

Question 7: Evaluate the product

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.

Question 9: Find , if for a unit

Question 10: Show that   is perpendicular to    ,for any two nonzero vectors a and b.

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

Question 12:If  are unit vectors such that , find the value of

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

Question 14:

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

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).

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

Question 17:  nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then  is unit vector if

(A) λ = 1

(B) λ = –1

(c) a = | λ|

(d) a = 1/| λ|

ANSWER :  Vector  is a unit vector if

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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## 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.

## Mathematics (Maths) Class 12

205 videos|264 docs|139 tests

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