Question

Find the projection of 𝑖 = (4, −1, 4) on 𝑗 = (−2, 0, 4).

Answer 1

Projection of i on j $=\dfrac{\vec{i}.\vec{j}}{|\vec{j}|}$

$=\dfrac{(4\hat{i}-\hat{j}+4\hat{k}).(-2\hat{i}+4\hat{k})}{\sqrt{(-2)^2+(4)^2}}$

$=\dfrac{-8+16}{\sqrt{4+16}}=\dfrac{8}{\sqrt{20}}=\dfrac{4\sqrt{5}}{5}$