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

The correct answer is: $\frac{60}{\sqrt{114}}$
Let $\vec{a}=\hat{i}+3\hat{j}+7\hat{k}$ on the vector $7\hat{i}-\hat{j}+8\hat{k}.$
Now,projection $\vec{a}$ on $\vec{b}$ is given by,
$\frac{1}{|\vec{b}|}(\vec{a}.\vec{b})=\frac{1}{\sqrt{7^2+(-1)^2+8^2}}[1(7)+3(-1)+7(8)]=\frac{7-3+56}{\sqrt{49+1+64}}=\frac{60}{\sqrt{114}}$