Question

If $A=(1,2,3)$, $B=(-2,4,\lambda )$ and $\angle AOB=\pi /2$ where $O$ is the origin then $\lambda$ is

• A. $6$
• B. $-6$
• C. $0$
• D. $-2$

Answer 1

The correct option is D $-2$

The vector OA is given by $i+2j+3k$ and vector OB is given by $-2i+4j+\lambda k$.

Since the angle between them is ${90}^0$ their dot product is zero.

Thus, we have $-2+8+3\lambda =0$

$\Rightarrow \lambda =-2$.