Question

If $3i+2j+8k$ and $2i+xj+k$ are at right angles then x =

• A. $7$
• B. $-7$
• C. $5$
• D. $-4$

Answer 1

Answer: (B)

$-7$

Let $\overrightarrow{a}=3\hat{i}+2\hat{j}+8\hat{k}$ and $\overrightarrow{b}=2\hat{i}+x\hat{j}+\hat{k}$
Given $\overrightarrow{a}$ and $\overrightarrow{b}$ are at right angles.
$\Rightarrow \overrightarrow{a}\cdot \overrightarrow{b}=0$
$\Rightarrow 6+2x+8=0$
$\therefore x=-7$
Hence, option B.