Scalar projection in the context of Unit vector

In mathematics, the scalar projection of a vector ${\displaystyle \mathbf {a} }$ on (or onto) a vector ${\displaystyle \mathbf {b} ,}$ also known as the scalar resolute of ${\displaystyle \mathbf {a} }$ in the direction of ${\displaystyle \mathbf {b} ,}$ is given by:

where the operator ${\displaystyle \cdot }$ denotes a dot product, ${\displaystyle {\hat {\mathbf {b} }}}$ is the unit vector in the direction of ${\displaystyle \mathbf {b} ,}$ ${\displaystyle \left\|\mathbf {a} \right\|}$ is the length of ${\displaystyle \mathbf {a} ,}$ and ${\displaystyle \theta }$ is the angle between ${\displaystyle \mathbf {a} }$ and ${\displaystyle \mathbf {b} }$.