Question

Find the cosine of the angle between the vectors $\overrightarrow{A}=(3\hat{i}+\hat{j}+2\hat{k})and\hat{B}=(2\hat{i}-2\hat{j}+4\hat{k}).$

• A. $\frac{3}{\sqrt{21}}$
• B. $\frac{\sqrt{12}}{\sqrt{21}}$
• C. $\frac{9}{\sqrt{21}}$
• D. $\frac{3}{\sqrt{12}}$

Answer 1

The correct option is A $\frac{3}{\sqrt{21}}$

$\overrightarrow{A}=3\hat{i}+\hat{j}+2\hat{k}\overrightarrow{B}=2\hat{i}-2\hat{j}+4\hat{k}\angle \overrightarrow{A}\overrightarrow{B}=\theta \cos \theta =\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|}=\frac{6-2+8}{\sqrt{14}\sqrt{24}}=\frac{12}{4\sqrt{21}}=\frac{3}{\sqrt{21}}$