Component of a vector along axes using angles for JEE

Formula

\(\vec{a}=|\vec{a}|(\cos\alpha\,\hat{i}+\cos\beta\,\hat{j}+\cos\gamma\,\hat{k})\)

Variables: \(\alpha,\beta,\gamma\) are angles made by \(\vec{a}\) with positive \(x\)-, \(y\)-, and \(z\)-axes.

Conditions: \(\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1\).

Problems involving angles a vector makes with axes.