# Scalar Projection Calculator

The calculator will find the scalar projection of one vector onto another, with steps shown.

Related calculator: Vector Projection Calculator

$$\mathbf{\vec{u}}$$$: ( , , ) $$\mathbf{\vec{v}}$$$: (
,
,
)
Hint: if you have two-dimensional vectors, set the third coordinates equal to or leave them empty.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Calculate the scalar projection of $$\mathbf{\vec{v}} = \left(7, 0, 5\right)$$$onto $$\mathbf{\vec{u}} = \left(1, -3, -4\right)$$$.
The scalar projection is given as $$\frac{\mathbf{\vec{u}}\cdot \mathbf{\vec{v}}}{\mathbf{\left\lvert\vec{u}\right\rvert}}$$$. $$\mathbf{\vec{u}}\cdot \mathbf{\vec{v}} = -13$$$ (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 $$\frac{\mathbf{\vec{u}}\cdot \mathbf{\vec{v}}}{\mathbf{\left\lvert\vec{u}\right\rvert}} = \frac{-13}{\sqrt{26}} = - \frac{\sqrt{26}}{2}.$$$
The scalar projection is $$- \frac{\sqrt{26}}{2}\approx -2.54950975679639$$\$A.