RD Sharma Solutions Class 12 Algebra Of Vectors Exercise 23.2

RD Sharma Solutions for Class 12 Maths Chapter 23 Algebra of Vectors Exercise 23.2 are enclosed here. Top subject-matter experts at BYJU’S have designed these solutions in a way that is easily understood by every student. Moreover, all the solutions are written in a simple stepwise format.  Here, the RD Sharma Class 12 Solutions to this exercise are contained in PDF format, which can be downloaded easily from the link given below.

Download PDF of Rd Sharma Solution for Class 12 Maths Chapter 23 Exercise 2

 

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Access Answers for Rd Sharma Solution Class 12 Maths Chapter 23 Exercise 2

Exercise 23.2

1. Solution:

Given that P, Q and R are collinear

Also, given that

RD Sharma Solutions for Class 12 Maths Chapter 23 - 11

2. Solution:

RD Sharma Solutions for Class 12 Maths Chapter 23 - 12

Given that,
RD Sharma Solutions for Class 12 Maths Chapter 23 - 13are the three sides of a triangle

So, we have

RD Sharma Solutions for Class 12 Maths Chapter 23 - 14

The triangle law says that, if vectors are represented in magnitude and direction by the two sides of triangle taken in same order, then their sum is represented by the third side taken in reverse order.

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 23 - 15

3. Solution:

Given that
RD Sharma Solutions for Class 12 Maths Chapter 23 - 16are two non-collinear vectors having the same initial point

Let
RD Sharma Solutions for Class 12 Maths Chapter 23 - 17, so we can draw a parallelogram ABCD as above

By the properties of parallelogram, we have

RD Sharma Solutions for Class 12 Maths Chapter 23 - 18

In ∆ABC,

Using triangle law, we have

RD Sharma Solutions for Class 12 Maths Chapter 23 - 19

Thus, from equations (i) and (ii), we get that

RD Sharma Solutions for Class 12 Maths Chapter 23 - 20

4. Solution:

Given, m is scalar and
RD Sharma Solutions for Class 12 Maths Chapter 23 - 21is a vector such that
RD Sharma Solutions for Class 12 Maths Chapter 23 - 22

Now,

RD Sharma Solutions for Class 12 Maths Chapter 23 - 23

On comparing the coefficients of unit vectors i, j and k of L.H.S and R.H.S, we have

RD Sharma Solutions for Class 12 Maths Chapter 23 - 24

5.(i) Solution:

Let

RD Sharma Solutions for Class 12 Maths Chapter 23 - 25

On comparing the coefficients of unit vectors i, j and k in L.H.S and R.H.S, we get

a1 = -a2 … (i)

b1 = – b2 … (ii)

c1 = – c2 … (iii)

RD Sharma Solutions for Class 12 Maths Chapter 23 - 26

(ii) Solution:

RD Sharma Solutions for Class 12 Maths Chapter 23 - 27

Given that a and b are two vectors such that

It means that the magnitudes of vector
RD Sharma Solutions for Class 12 Maths Chapter 23 - 28are equal to the magnitude of vector
RD Sharma Solutions for Class 12 Maths Chapter 23 - 29, but we cannot conclude anything about the direction of vectors.

So, it is false that

RD Sharma Solutions for Class 12 Maths Chapter 23 - 30

(iii) Solution:

Given that for any vector
RD Sharma Solutions for Class 12 Maths Chapter 23 - 31

RD Sharma Solutions for Class 12 Maths Chapter 23 - 32

It means that the magnitudes of vector
RD Sharma Solutions for Class 12 Maths Chapter 23 - 33are equal to the magnitude of vector
RD Sharma Solutions for Class 12 Maths Chapter 23 - 34, but we cannot conclude anything about the direction of vectors.

Moreover, we know that only when
RD Sharma Solutions for Class 12 Maths Chapter 23 - 35means, both the direction and magnitude are the same for both the vectors. Hence, the given statement is false.

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