Question

The projection of $\vec{a}=3\hat{i}-\hat{j}+5\hat {k} $ on $\vec{b}=2 \hat {i}+3 \hat j+\hat k$ is

• A. $\frac {8}{\sqrt {35}}$
• B. $\frac {8}{\sqrt {39}}$
• C. $\frac {8}{\sqrt {14}}$
• D. $\sqrt {14}$

Answer 1

Answer: (C)

Given, $\vec{a} =3 \hat{i} - \hat{j} + 5 \hat{k}\,\,\,\, $ and $\,\,\,\,\vec{b} =2 \hat{i} + 3 \hat{j} + \hat{k} $
The projection of $ \vec{a} $ on $\vec{b} = \frac{\vec{a} . \vec{b}}{\left|\vec{b}\right|}$
$ = \frac{\left(3 \hat{i} - \hat{j} + 5 \hat{k}\right). \left(2 \hat{i} + 3 \hat{j} + \hat{k}\right)}{\sqrt{2^{2} + 3^{2} +1^{2}}} $
$= \frac{6-3+5}{\sqrt{14}} = \frac{8}{\sqrt{14}} $