Question

If the line joining the points $(-1,2,3),(2,-1,4)$ is perpendicular to the line joining the points $(x,-2,4),(1,2,3)$ then $x=$.

• A. $3$
• B. $10$
• C. $\frac{-3}{10}$
• D. $\frac{-10}{3}$

Answer 1

Answer: (D)

$\frac{-10}{3}$

line joining $(-1,2,3)$ & $(2,-1,4)$

$\overrightarrow{a}=3\hat{i}-3\hat{j}+\hat{k}$

line joining $(x,-2,4)$ & $(1,2,3)$

$\overrightarrow{b}=(1-x)\hat{i}+4\hat{j}-\hat{k}$

$\therefore \overrightarrow{a}$ and $\overrightarrow{b}$ to be $\perp$ $\overrightarrow{a}.\overrightarrow{b}=0$

$\therefore (3\hat{i}-3\hat{j}+\hat{k}).\left(\right(1-x)\hat{i}+4\hat{j}-\hat{k})=03(1-x)-2-1=0\Rightarrow x=\frac{-10}{3}$