Dot Product Formula

There are two equivalent formulas for the dot product of vectors $vec{a}$ and $vec{b}$.

Component form

$vec{a} cdot vec{b} = a_1 b_1 + a_2 b_2 + a_3 b_3$.

Geometric form

$vec{a} cdot vec{b} = |vec{a}||vec{b}| cos theta$, where $theta$ is the angle between the two vectors.

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