Question

Find the projection of the vector $\hat{i}+3\hat{j}+7\hat{k}$ on the vector $7\hat{i}-\hat{j}+8\hat{k}$.

Answer 1

Let

$\overrightarrow{a}=\hat{i}+3\hat{j}+7\hat{k}$

And, $\overrightarrow{b}=7\hat{i}-\hat{j}+8\hat{k}$.

Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by

$\frac{1}{|b|}(\overrightarrow{a}.\overrightarrow{b})$

$=\frac{1}{\sqrt{7^2+1^2+8^2}}(7-3+56)$

$=\frac{60}{\sqrt{114}}$