# Scalar projection of $\left\langle -2, 5, -1\right\rangle$ onto $\left\langle -10, 7, -1\right\rangle$

The calculator will find the scalar projection of the vector $\left\langle -2, 5, -1\right\rangle$ onto the vector $\left\langle -10, 7, -1\right\rangle$, with steps shown.

Related calculator: Vector Projection Calculator

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Calculate the scalar projection of $\mathbf{\vec{v}} = \left\langle -2, 5, -1\right\rangle$ onto $\mathbf{\vec{u}} = \left\langle -10, 7, -1\right\rangle$.

### Solution

The scalar projection is given by $\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}}$.

$\mathbf{\vec{v}}\cdot \mathbf{\vec{u}} = 56$ (for steps, see dot product calculator).

$\mathbf{\left\lvert\vec{u}\right\rvert} = 5 \sqrt{6}$ (for steps, see vector magnitude calculator).

Thus, the scalar projection is $\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}} = \frac{56}{5 \sqrt{6}} = \frac{28 \sqrt{6}}{15}.$

The scalar projection is $\frac{28 \sqrt{6}}{15}\approx 4.572380853195266$A.