Question

The angle between the two vectors $-2\hat{i}+3\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}-4\hat{k}$ is:

• A. 0${}^o$
• B. 90${}^o$
• C. 180${}^o$
• D. 45${}^o$

Answer 1

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

The angle between the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is
$cos\theta =\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{\left|\overrightarrow{A}\overrightarrow{B}\right|}$
$\overrightarrow{A}\cdot \overrightarrow{B}$ = $(-2i+3\overline{j}+\overline{k})\cdot (i+2\overline{j}-4\overline{k})=-2+6-4=0$
$\overrightarrow{A}=\sqrt{(2{)}^2+(3{)}^2+(1{)}^2}=\sqrt{14}$
$\overrightarrow{B}=\sqrt{(1{)}^2+(2{)}^2+(4{)}^2}=\sqrt{21}$
$cos\theta =\frac{0}{\sqrt{14}\sqrt{21}}$ or $\theta ={90}^0$