Question

The projection $2\hat{i}+3\hat{j}-2\hat{k}$ on the vector $\hat{i}+2\hat{j}-3\hat{k}$ is

• A. $\frac{1}{\sqrt{14}}$
• B. $\sqrt{14}$
• C. $\frac{2}{\sqrt{14}}$
• D. none of these

Answer 1

The correct option is B $\sqrt{14}$

Projection of $\overline{a}$ on $\overline{b}$ is a cos$\theta$ where $\theta$ is the angle between the two.
Let $\overline{a}=2\hat{i}+3\hat{j}-2\hat{k}$ and $\overline{b}=\hat{i}+2\hat{j}-3\hat{k}$
$cos\theta =\frac{2+6+6}{\sqrt{17}\times \sqrt{14}}$
Thus projection = $(2+6+6)/\sqrt{14}=\sqrt{14}$