Question

Let $P=(1,0,-1)$ $Q=(-1,2,0)$ $R=(2,0,-3)$ and $S=(3,-2,-1)$, then the length of the components of RS on PQ is?

• A. $1/3$
• B. $2/3$
• C. $4/3$
• D. $5/3$

Answer 1

The correct option is C $4/3$

$\begin{array}{c}\overrightarrow{RS}=\overrightarrow{OS}-\overrightarrow{OR}=\hat{i}-2\hat{j}+2\hat{k}\\ \\ \overrightarrow{PQ}=\overrightarrow{OQ}-\overrightarrow{OP}=-2\hat{i}+2\hat{j}+\hat{k}\\ \\ \left|\overrightarrow{PQ}\right|=\sqrt{{\left(-2\right)}^2+{\left(2\right)}^2+{\left(1\right)}^2}=3\end{array}$

So, component of $RS$ on $PQ=|\frac{\overrightarrow{RS}.\overrightarrow{PQ}}{|\overrightarrow{PQ}|}|$

Component of RS on PQ $=\left|\frac{\left(\hat{i}-2\hat{j}+2\hat{k}\right).\left(-2\hat{i}+2\hat{j}+\hat{k}\right)}{3}\right|=\frac{4}{3}$

Hence the option $C$ is correct answer.