Question

The position vector of a point C with respect to B is $\mathbf{i} + \mathbf{j}$ and that of B with respect to A is $\mathbf{i} - \mathbf{j}.$ The position vector of C with respect to A is

• A. 2 i
• B. 2 j
• C. – 2 j
• D. – 2 i

Answer 1

Answer: (A)

2 i

Answer 2

Since position vector of a point $C$ with respect to $B$ is

$\overset{\rightarrow}{BC} = \mathbf{i} + \mathbf{j}$ …..(i)

Similarly, $\overset{\rightarrow}{AB} = \mathbf{i} - \mathbf{j}$ …..(ii)

Now by (i) and (ii), $\overset{\rightarrow}{AC} = \overset{\rightarrow}{AB} + \overset{\rightarrow}{BC} = 2\mathbf{i}.$