Scalar and Vector Projections of One Vector onto Another

Rarely Tested

Scalar projection of $$\vec{a}$$ on $$\vec{b}$$:

$$\mathrm{comp}_{\vec b}\vec a = \frac{\vec a \cdot \vec b}{|\vec b|}$$

Vector projection of $$\vec{a}$$ on $$\vec{b}$$:

$$\mathrm{proj}_{\vec b}\vec a = \frac{\vec a \cdot \vec b}{|\vec b|^2}\,\vec b = (\vec a \cdot \hat{\vec b})\,\hat{\vec b}$$
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