Question

If the angle between two lines whose d.rs are $2,3,-1$ and $0,k,-2$ is ${90}^o$, then $k=$

• A. $\frac{-3}{2}$
• B. $\frac{-2}{3}$
• C. $\frac{2}{3}$
• D. $\frac{-1}{3}$

Answer 1

The correct option is B $\frac{-2}{3}$

Since lines are perpendicular, their dot product must be zero.
$\therefore 2\times 0+3\times k+(-2)\times (-1)=0$
$\therefore 3k=-2$
$\therefore k=\frac{-2}{3}$