= Scalar projection
{title2=$\operatorname{comp}_{\mathbf c}\mathbf a=\mathbf a\cdot\mathbf c/\|\mathbf c\|$}
{wiki}
The <scalar projection> of a real <Euclidean vector> $\mathbf a$ onto a nonzero <Euclidean vector> $\mathbf c$ is its signed component along the <unit vector> $\mathbf c/\|\mathbf c\|$:
$$
\operatorname{comp}_{\mathbf c}\mathbf a=\mathbf a\cdot\frac{\mathbf c}{\|\mathbf c\|}.
$$
For $\mathbf a=(3,4)$, the <scalar projection> onto $(2,0)$ is $3$, while that onto $(-2,0)$ is $-3$. Reversing the measuring direction reverses the sign; the <scalar projection> is not necessarily a nonnegative length. For nonzero $\mathbf a$, it also equals $\|\mathbf a\|\cos\theta$, using the <angle> with $\mathbf c$ and its <cosine>. For the <zero vector> it is zero, even though that <angle> is undefined.
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