Scalar projection is vector length times cosine of angle

The scalar projection of a vector \(\vec a\) onto a vector \(\vec b\) can be found if the vector_length of \(\vec a\) and the angle between \(\vec a\) and \(\vec b\) are known.

Links:

  1. Wikipedia.

angle

angle between \(\vec a\) and \(\vec b\).

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

vector_length

Length of the projected vector \(\vec a\).

Symbol:

a

Latex:

\(a\)

Dimension:

any_dimension

projection

Length of the projection of \(\vec a\) onto \(\vec b\).

Symbol:

s

Latex:

\(s\)

Dimension:

any_dimension

law

s = a * cos(phi)

Latex:
\[s = a \cos{\left(\varphi \right)}\]