Question

If $\overrightarrow{A}=2i+3j$ and $\overrightarrow{B}=2\hat{j}+3\hat{k}$ the component of $\overline{B}$ along $\overline{A}$ is

• A. 6
• B. 1/6
• C. 6/13
• D. $\frac{6}{\sqrt{13}}$

Answer 1

The correct option is D $\frac{6}{\sqrt{13}}$

$\begin{array}{c}\overrightarrow{A}=2\hat{i}+3\hat{j}\overrightarrow{B}=2\hat{j}+3\hat{k}\\ \cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{\left|A\right|\left|B\right|}=\frac{6}{\sqrt{13}\times \sqrt{13}}=\frac{6}{13}\\ \therefore component:B\cos \theta \\ =\sqrt{13}.\frac{6}{13}\\ =\frac{6}{\sqrt{13}}\end{array}$

$\therefore$ Option $D$ is correct .