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The vector projection of the vector v onto a non-zero vector d is the component of v that is parallel to d. In mathematical terms,

$ \mathrm{proj}_\vec{d} \vec{v} = \frac{ \vec{v} \cdot \vec{d}}{\| \vec{d} \|^2 } \vec{d} = \frac{ \vec{v} \cdot \vec{d}}{\| \vec{d} \| } \hat{d} $

where $ \hat{d} $ is the unit vector in the direction of d. The projection can also be used to find component of v normal (or orthogonal) to d as follows:

$ \vec{v}_n = \vec{v} - \mathrm{proj}_\vec{d} \vec{v} $
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