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

Answer: (B)

Let $a=i-2j+k$ and $b=4i-4j+7k$, then projection of $a$ on $b$ is equal to
$\frac{a.b}{|b|}=\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{9}$