Scalar Projection Calculator

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

Related calculator: Vector Projection Calculator

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Your Input

Calculate the scalar projection of $$$\mathbf{\vec{v}} = \left(7, 0, 5\right)$$$ onto $$$\mathbf{\vec{u}} = \left(1, -3, -4\right)$$$.

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 $$$\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}} = \frac{-13}{\sqrt{26}} = - \frac{\sqrt{26}}{2}.$$$

Answer

The scalar projection is $$$- \frac{\sqrt{26}}{2}\approx -2.549509756796392$$$A.