Question

The position vector of mid-point lying on the line joining the points whose positions vectors are $i+j-k$ and $i-j+k$ is?

• A. $i$
• B. $j$
• C. $k$
• D. $0$

Answer 1

The correct option is A

$i$

Explanation for the correct option:

Find the position vector of the required mid-point

In the question, the position vector $i+j-k$ and $i-j+k$ of two-point is given.

Since It is required to find the position vector of the mid-point of the line formed by joining the given points.

So, the mid-point of the line is also the mid-point of the given points.

Therefore, the required position vector is given by:

$\frac{(i+i)}{2}+\left[\frac{j+(-j)}{2}\right]+\left[\frac{-k+k}{2}\right]=i$

Therefore, The position vector of the mid-point lying on the line joining the points whose positions vectors are $i+j-k$ and $i-j+k$ is $i$.

Hence, option $A$, $i$ is the correct answer.