Question

$\overrightarrow{A}=2\hat{i}+4\hat{j}+4\hat{k}$ and $\overrightarrow{B}=4\hat{i}+2\hat{j}-4\hat{k}$ are two vectors. The angle between them will be

• A. $0^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

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

$\cos \theta =\frac{\overrightarrow{A}..\overrightarrow{B}}{|\overrightarrow{A}|.|\overrightarrow{B}|}=\frac{a_1{b}_2+a_2{b}_2+a_3{b}_3}{|\overrightarrow{A}|.|\overrightarrow{B}|}$
$=\frac{2\times 4+4\times 2-4\times 4}{|\overrightarrow{A}|.|\overrightarrow{B}|}=0$
$\therefore \theta ={\cos }^{-1}\left(0^o\right)\Rightarrow \theta ={90}^o$