Question

The magnitude of the component of the vector$(2\hat{i}+3\hat{j}+\hat{k})$ along $(3\hat{i}+4\hat{k})$ is :

• A. 1$/2$
• B. 14$/5$
• C. $3$
• D. $2$

Answer 1

The correct option is D $2$

$\begin{array}{c}Let\overrightarrow{A}=\left(2\hat{i}+3\hat{j}+\hat{k}\right)\\ \overrightarrow{B}=\left(3\hat{i}+4\hat{k}\right)\\ \therefore Magnitudeof\hat{A}along\hat{B}=\frac{\hat{A}.\hat{B}}{\left|\hat{B}\right|}\\ =\frac{\left(2\hat{i}+3\hat{j}+\hat{k}\right)\left(3\hat{i}+4\hat{k}\right)}{\sqrt{3^2+4^2}}\\ =\frac{6+0+4}{\sqrt{9+16}}=\frac{10}{\sqrt{125}}\\ =\frac{10}{5}=2\end{array}$

Hence, Option $D$ is correct.