Question

The projection of the vector $\hat{i}-2\hat{j}+\hat{k}$ on the vector $4\hat{i}-4\hat{j}+7\hat{k}$ is

• A. $\frac{5\sqrt{6}}{10}$
• B. $\frac{19}{9}$
• C. $\frac{9}{19}$
• D. $\frac{\sqrt{6}}{19}$

Answer 1

The correct option is B $\frac{19}{9}$

Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$
$=|a|\cos \theta =|a|\frac{a\cdot b}{|a||a|}=\frac{a\cdot b}{|b|}$

$=\frac{4+8+7}{\sqrt{16+16+49}}$

$=\frac{19}{\sqrt{81}}$

$=\frac{19}{9}$