Scalar Projection Calculator
The calculator will find the scalar projection of one vector onto another, with steps shown.
Related calculator: Vector Projection Calculator
Your Input
Calculate the scalar projection of $$$\mathbf{\vec{v}} = \left\langle 7, 0, 5\right\rangle$$$ onto $$$\mathbf{\vec{u}} = \left\langle 1, -3, -4\right\rangle$$$.
Solution
The scalar projection is given by $$$\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}}$$$.
$$$\mathbf{\vec{v}}\cdot \mathbf{\vec{u}} = -13$$$ (for steps, see dot product calculator).
$$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{26}$$$ (for steps, see vector magnitude calculator).
Thus, the scalar projection is $$$\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}} = \frac{-13}{\sqrt{26}} = - \frac{\sqrt{26}}{2}.$$$