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 given here. Top subject-matter experts at BYJU’S have designed these solutions in a way that is easily understandable 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 given in PDF format, which can be downloaded easily from the link given below.

RD Sharma Solution for Class 12 Maths Chapter 23 Exercise 2

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Exercise 23.2

1. Solution:

Given that P, Q and R are collinear

Also, given that

2. Solution:

Given that,
are the three sides of a triangle

So, we have

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

Therefore,

3. Solution:

Given that
are two non-collinear vectors having the same initial point

Let
, so we can draw a parallelogram ABCD as above

By the properties of a parallelogram, we have

In ∆ABC,

Using triangle law, we have

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

4. Solution:

Given m is scalar and
is a vector such that

Now,

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

5.(i) Solution:

Let

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)

(ii) Solution:

Given that a and b are two vectors such that

It means that the magnitudes of vector
are equal to the magnitude of the vector
, but we cannot conclude anything about the direction of vectors.

So, it is false that

(iii) Solution:

Given that for any vector

It means that the magnitudes of vector
are equal to the magnitude of the vector
, but we cannot conclude anything about the direction of vectors.

Moreover, we know that only when
means both the direction and magnitude are the same for both vectors. Hence, the given statement is false.