If a⃗ = 2î + ĵ + 2k̂ and b⃗ = 5î - 3ĵ + k̂, find the projection of b⃗ on a⃗.

If $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b} = 5\hat{i} - 3\hat{j} + \hat{k}$, find the projection of $\vec{b}$ on $\vec{a}$.

Answer

Projection of $\vec b$ on $\vec a = \frac{\vec a\cdot\vec b}{|\vec a|} = \frac{10 - 3 + 2}{\sqrt{4+1+4}} = \frac{9}{3} = 3$ units.