Question

The projection of $\mathbf{a} = 2\mathbf{i} + 3\mathbf{j} - 2\mathbf{k}$ on $\mathbf{b} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$ is

• A. $\frac{1}{\sqrt{14}}$
• B. $\frac{2}{\sqrt{14}}$
• C. $\sqrt{14}$
• D. $\frac{- 2}{\sqrt{14}}$

Answer 1

Answer: (B)

$\frac{2}{\sqrt{14}}$

Answer 2

Projection of $\mathbf{a}$ on $\mathbf{b}$ = $\mathbf{a}.\widehat{\mathbf{b}} = \mathbf{a}.\frac{\mathbf{b}}{|\mathbf{b}|}$

= $\frac{(2\mathbf{i} + 3\mathbf{j} - 2\mathbf{k}).(\mathbf{i} + 2\mathbf{j} + 3\mathbf{k})}{|\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}|}$ = $\frac{2 + 6 - 6}{\sqrt{14}} = \frac{2}{\sqrt{14}}$