Question

The angle between the two vectors $\overrightarrow{A}=\hat{i}+2\hat{j}-\hat{k}$ and $\overrightarrow{B}=-\hat{i}+\hat{j}-2\hat{k}$ is:

• A. ${90}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

Answer: (D)

${60}^o$

Angle between two vectors is given as $\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$

$\cos \theta =\frac{(\hat{i}+2\hat{j}-\hat{k}).(-\hat{i}+\hat{j}-2\hat{k})}{\sqrt{1^2+2^2+1^2}\times \sqrt{1^2+1^2+2^2}}$

$\cos \theta =\frac{(-1+2+2)}{\sqrt{6}\times \sqrt{6}}$

$\cos \theta =\frac{3}{6}=\frac{1}{2}$

$\Rightarrow \theta ={60}^{\circ }$