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The RD Sharma mathematics collection is said to be the topmost solution for students to prepare themselves for board examinations. The CBSE students are most likely to get recommended by their teachers to get help from the RD Sharma class 12 solution of Algebra of vectors exercise VSA to guide for better understanding. RD Sharma solutions Therefore, without a doubt, any student can opt for the RD Sharma class 12th exercise VSA for a better understanding of maths.

Algebra of Vectors Exercise Very Short Answer Question 1

Given: Define Zero vectorExplanation:

A vector whose initial and final point coincident or the length of vector is zero known as zero vector or null vector. The null vector is denoted by . Also, the magnitude of zero vector is same.

Algebra of Vectors Exercise Very Short Answer Question 2

Given: Define Unit vectorExplanation:

A unit vector is a vector that has a magnitude of 1. The unit vector in the direction of a vector is denoted by

Algebra of Vectors Exercise Very Short Answer Question 3

Explanation:

The position vector is said to be a straight line having one end fixed to a body like origin and the second end that is attached to a moving point and this is used to describe the position of the point relative to the body.

A point O is fixed as origin in space (or plane) and P is any point, then

is called a position vector of P w.r.t O

Algebra of Vectors Exercise Very Short Answer Question 4

Given: Write in simplest form

Solution: We have,

because of change in direction

Hence

Algebra of Vectors Exercise Very Short Answer Question 5

Answer:Hint: You must know the rules of vector functions.

Given: If and are two non-collinear vectors, such that , then write the values of and

Solution: We have, and are non-collinear vectors and

Given that and are non collinear , so and should not be parallel ,

Therefore,

Similarly , the given equation can also be written as

Given that and are non collinear , so and should not be parallel ,

Therefore,

Hence we get , and

Algebra of Vectors Exercise Very Short Answer Question 6

Answer:Hints: You must know the rules of vector functions.

Given: If and represents two adjacent sides of a parallelogram, then write vectors representing its diagonals.

Solution:

Let and represents two adjacent sides of a parallelogram ABCD.

∴ AB = DC and AD = BC [Because diagonals of parallelogram is equal]

In ABC

Now, In ABD

Vectors representing its diagonals are

Algebra of Vectors Exercise Very Short Answer Question 7

Answer:Hint: You must know the rules of vector functions.

Given: If represents the sides of a triangle taken in order, then write the value of

Solution: Let ABC be a triangle, such that

Then,

Algebra of Vectors Exercise Very Short Answer Question 8

Answer:Hint: You must know the rules of vector functions.

Given: If are position vectors of vertices A, B and C respectively of a triangle ABC, write the value of

Solution: Given are position vectors of vertices A, B and C respectively

Then,

Consider,

Algebra of Vectors Exercise Very Short Answer Question 9

Answer:Hint: You must know the rules of vector functions.

Given: If are position vectors of points A, B and C respectively, write the value of

Solution: are position vectors of points A, B and C respectively.

Then,

Therefore,

Algebra of Vectors Exercise Very Short Answer Question 10

Answer:Hint: You must know the rules of vector functions

Given: If are position vectors of vertices of a triangle, then write the position vector of centroid.

Solution: Let ABC be a triangle and D,E and F are the mid-points of sides BC, CA and AB respectively.

Also, Let are position vectors of A, B, C respectively.

Then position vectors of D, E and F are

respectively.

The position vector of a point divides AD in the ratio of 2 is

Similarly, position vectors of the points divides BE, CF in the ratio of 2:1 are equal to

Thus, the points dividing AD in ratio 2:1 also divides BE, CF in the ratio.

Hence, medians of triangle are concurrent and the position of centroid is

Algebra of Vectors Exercise Very Short Answer Type Question 11

Answer:Hint: You must know the rules of vector functions

Given: If G is denotes the centroid of ?ABC , then write the value of

Solution: Let be the position vectors of the vertices A, B and C respectively.

Then, the position of centroid G is

Thus,

Algebra of Vectors Exercise Very Short Answer Type Question 12

Answer:Hint: You must know the rules of vector functions

Given: If & denote the position vectors of points A and B respectively and C is appoint on AB, such that 3AC = 2AB, then write the position vector of C

Solution: Let is the position vector of c

Now,

Consider,

Algebra of Vectors Exercise Very Short Answer Type Question 13

Hint: You must know the rules of vector functions

Given: If D is the mid-point of sides BC of a triangle ABC such find

Solution: D is mid-point of side BC of a ABC,

Let is a position vectors of AB, BC, CA

Now, the position vector of D is

Then,

Algebra of Vectors Exercise Very Short Answer Type Question 14

Answer:Hint: You must know the rules of vector functions

Given: If D,E, F are the mid-points of sides BC,CA and AB respectively of

Write the value of

Solution: D, E, F are the mid-points of sides BC, CA, AB respectively

Then, the position vectors of the mid-points

D, E, F are given by

Now,

Algebra of Vectors Exercise Very Short Answer Type Question 15

Answer:Hint: You must know the rules of vector functions

Given: If is a non-zero vector of modulus a and m is a non-zero scalar such that is a unit vector, find m.

Solution: is non-zero vector with modulus a and m

Also is unit vector

Therefore,

Algebra of Vectors Exercise Very Short Answer Type Question 16

Answer:Hint: You must know the rules of vector functions

Given: If are the position vectors of the vertices of equilateral triangle. Write value of

Solution: Let ABC be a given equilateral triangle and vertices are . Also be your orthocentre.

We know the centroid and orthocenter of equilateral triangles coincide at a point.

Orthocentre of

Centroid of

Algebra of Vectors Exercise Very Short Answer Type Question 17

A nswer:

Hint: You must know the rules of vector functions

Given: Write a unit vector making equal acute angles with the coordinate axes

Solution: Suppose makes an angle with each of the axes OX, OY and OZ

Then its direction cosines are

Now,

Since, we know angle is acute, Hence we only take positive values

∴ Unit vector is

Algebra of Vectors Exercise Very Short Answer Type Question 18

Answer: 2Hint: You must know the rules of vector functions

Given: If a vector makes angles with & with OX, OY and OZ respectively, Write

Solution: Suppose, a vector makes angles & with OX, OY and OZ respectively

Then direction cosines of vectors are given by

Consider,

Algebra of Vectors Exercise Very Short Answer Type Question 19

Answer:Hint: You must know the rules of vector functions

Given: Write a vector of magnitude 12 units which makes angles with x-axis, angle with y-axis, obtuse angle with z- axis.

Solution: Suppose a vector makes an angle with OX, with OY and having magnitude 12 units.

Now,

But angle obtuse angle along z-axis, so we use negative value.

∴

Therefore,

Algebra of Vectors Exercise Very Short Answer Type Question 20

Answer: 13Hint: You must know the rules of vector functions

Given: Whose projections on coordinate axis are 12, 3, 4 units. Write length of vector

Solution:Projections on coordinate axis are 12, 3, 4 units

Therefore, length of vector

Algebra of Vectors Exercise Very Short Answer Type Question 21

Answer:Hint: You must know the rules of vector functions

Given: Write the position vector of a point dividing the line segment joining points A and B with position vectors & externally in the ratio 1:4 , where,

Solution: The position vectors of A and B are

Let C divides AB in the ratio such that AB:CB=1:4

Position vector of C=

Algebra of Vectors Exercise Very Short Answer Type Question 22

Answer:

Hint: You must know the rules of vector functions

Solution:

The direction cosines are

Algebra of Vectors Exercise Very Short Answer Type Question 23

Answer:Hint: You must know the rules of vector functions

Given: find unit vector parallel to

Solution:

Now,

Unit vector parallel to,

Algebra of Vectors Exercise Very Short Answer Type Question 24

Answer:Hint: You must know the rules of vector functions

Given: , find unit vector

Solution:

Hence,

Hence, unit vector along,

Algebra of Vectors Exercise Very Short Answer Type Question 25

Answer:Hint: You must know the rules of vector functions

Given: Find position vector of point dividing line segment

Externally in 2:3

Solution: Let A and B be the points with vectors

respectively

Let C divide AB externally with ratio 2:3 such AC: CB=2:3

Position vector of C=

Algebra of Vectors Exercise Very Short Answer Type Question 26

Answer:Hint: You must know the rules of vector functions

Given: find unit vector in the direction of

Solution:

Then,

Therefore, unit vector in the direction of

Algebra of Vectors Exercise Very Short Answer Type Question 27

Answer:Hint: You must know the rules of vector functions

Given: If

Solution:

Now,

Hence,

Algebra of Vectors Exercise Very Short Answer Type Question 28

Answer:Hint: You must know the rules of vector functions

Given: A unit vector make angles with & and an acute angle with .find

Solution: Angle with &

Let l , m , n be the direction cosines

Now,

But we know angle made with is an acute angle so, we use the positive value.

Algebra of Vectors Exercise Very Short Answer Type Question 29

Answer:Hint: You must know the rules of vector functions

Given: Find unit vector in direction of

Solution: We have,

Unit vector in direction of is

Algebra of Vectors Exercise Very Short Answer Type Question 30

Answer:Hint: You must know the rules of vector functions

Given: and find vector parallel to

Solution:

Now,

Vector parallel to

Algebra of Vectors Exercise Very Short Answer Type Question 31

Answer:Hint: You must know the rules of vector functions

Given: Find unit vector in direction of

Solution:

Unit vector:

Algebra of Vectors Exercise Very Short Answer Type Question 32

Answer:Hint: You must know the rules of vector functions

Given: Find the position vector of mid-point of line AB where

Solution:

Let C is the mid-point

∴ Position vector of

Hence position vector

Algebra of Vectors Exercise Very Short Answer Type Question 33

Answer:Hint: You must know the rules of vector functions

Given: Find a vector in direction of , which has magnitude 6 units

Solution:

Vector in direction of

Algebra of Vectors Exercise Very Short Answer Type Question 34

Answer:Hint: You must know the rules of vector functions

Given: What is the cosine of angle with vector makes with y – axis

Solution:

Direction cosines are

∴ Cosine angle along y-axis is

Algebra of Vectors Exercise Very Short Answer Type Question 35

Answer: Both have the same magnitude.Hint: You must know the rules of solving vectors

Given: Write two different vectors having same magnitude

Solution:

Let

Hence, both vectors are having the same magnitude.

Algebra of Vectors Exercise Very Short Answer Type Question 36

Answer:Hint: You must know the rules of vector functions

Given: Write two different factors having same direction

Solution:

Let

The direction cosines of is

And direction cosines of is

The direction cosines of and are same.

Algebra of Vectors Exercise Very Short Answer Type Question 37

Answer:Hint: You must know the rules of vector functions

Given: Write a vector in direction of having magnitude 8 units

Solution: Let

Position vector in the direction of vector is,

Algebra of Vectors Exercise Very Short Answer Type Question 38

Answer:

Hint: You must know the rules of vector functions

Given: , find direction cosines

Solution: Let

Hence direction cosines are,

Algebra of Vectors Exercise Very Short Answer Type Question 39

Answer:Hint: You must know the rules of vector functions

Given: Find unit vector in direction of

Solution:

Unit vector,

Algebra of Vectors Exercise Very Short Answer Type Question 40

Answer:Hint: You must know the rules of vector functions

Given: For what value of ‘a’ the vectors &are collinear

Solution: Two vectors are

Vectors are collinear,

By comparing

Hence

Algebra of Vectors Exercise very Short Answer type Question 41

Answer:Hint: You must know the rules of vector functions

Given: Find direction cosines of

Solution: Let

Then its cosines are,

Algebra of Vectors Exercise Very Short Answer Type Question 42

Answer:Hint: You must know the rules of vector functions

Given: Find sum of

So, sum of three vectors

Algebra of Vectors Exercise very Short Answer type Question 43

Answer:Hint: You must know the rules of vector functions

Given: Find unit vector in direction of

Solution:

Unit vector

Algebra of Vectors Exercise very Short Answer type Question 44

Answer:Hint: You must know the rules of vector functions

Given: If are two equal vectors find

Solution:

They are equal vectors, So,

By comparing

Algebra of Vectors Exercise very Short Answer type Question 45

Answer:Hint: You must know the rules of vector functions

Given: Find unit vector in direction of sum of vectors

Solution: We have,

Sum,

∴Required unit vector

Algebra of Vectors Exercise very Short Answer type Question 46

Answer:Hint: You must know the rules of vector functions

Given: Find value of ‘p’

are parallel

Solution:

Let

If & are parallel

On comparing,

Algebra of Vectors Exercise very Short Answer type Question 47

Hint: You must know the rules of vector functions

Given: Find a vector of magnitude ,making angle with x- axis, with y-axis and with z-axis

Solution: with x- axis, with y-axis and with z-axis

Since is an acute angle

Now,

Algebra of Vectors Exercise very Short Answer type Question 48

Answer:Hint: You must know the rules of vector functions

Given: Find a unit vector in direction of when &

Solution: &

Unit Vector:

Algebra of Vectors Exercise very Short Answer type Question 49

Answer:Hint: You must know the rules of vector functions

Given: Find vector in direction of having magnitude 21 units

Solution: Let

Unit vector

We know, magnitude is 21 units

Algebra of Vectors Exercise very Short Answer type Question 50

Answer:Hint: You must know the rules of vector functions

Given: If and , Writer range of

Solution:

Value of

Range of

Algebra of Vectors Exercise very Short Answer type Question 51

Answer:Hint: You must know the rules of vector functions

Given: , if B is mid-point of AC and ,find

Solution:

Algebra of Vectors Exercise very Short Answer type Question 52

Answer:Hint: You must know the rules of vector functions

Given: Write the position vector of the point which divides the join of points with position vectors & in ratio 2:1

Solution: Let R be the point which divides the line joining point with vectors.

& in ratio 2:1

And

Here

Position vector of is as follows

Class 12 RD Sharma chapter 22 exercise VSA solution deals with the chapter of Algebra of vectors, which might be a complex chapter for some students to solve. So RD Sharma class 12th exercise VSA provides you with very short answer type questions to take a self-test and evaluate your performance accordingly. The RD Sharma class 12 solutions chapter 22 exercise VSA consists of a total of 52 questions that covers all the essential concepts of the chapter mentioned below-

Zero vector

Unit vector

Position vector

Vectors in simplified form

Centroid

Direction Cosines

Vectors with same magnitude and direction

Listed below are a few reasons why the RD Sharma class 12th exercise VSA is helpful in the preparation of exams:-

The questions have a good proportion chance to be asked in the board exams because the exercises designed in the RD Sharma solution cover up each and every concept of every chapter

The RD Sharma class 12th exercise VSA consists of questions that are frequently asked in board exams so students have to go through each and every exercise thoroughly.

The solution also helps in solving the homework as it provides you with solved questions and examples and also because teachers use the solutions to assign homework.

The RD Sharma class 12 chapter 22 exercise VSA is trusted by many students across the country as they have seen that a good practice of the RD Sharma solution has helped them to score big.

The best part about RD Sharma class 12th exercise VSA is students can download the solutions free of cost from the Career360 website.

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