Question

Angle between the vectors $\overrightarrow{a}=-\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{b}=x\hat{i}+\hat{j}+(x-2)\hat{k}$

• A. is obtuse angle
• B. is acute angle
• C. is ${90}^o$
• D. depends upon x

Answer 1

The correct option is C is ${90}^o$

$\overrightarrow{a}=-\hat{i}+2\hat{j}+\hat{k}$
$\overrightarrow{b}=x\hat{i}+\hat{j}+(x-2)\hat{k}$
$cos\theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}$
$cos\theta =\frac{-x+2+x-2}{ab}$
$cos\theta =0$
$\theta ={90}^o$