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

Now, projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by,

$\frac{1}{|\overrightarrow{b}|}(\overrightarrow{a}\cdot \overrightarrow{b})=\frac{1}{\sqrt{7^2+(-1{)}^2+8^2}}\left\{1\right(7)+3(-1)+7(8\left)\right\}=\frac{7-3+56}{\sqrt{49+1+64}}=\frac{60}{\sqrt{114}}$