# Scalar projection of $\left\langle 5, -1, 2\right\rangle$ onto $\left\langle 4, 4, -3\right\rangle$

The calculator will find the scalar projection of the vector $\left\langle 5, -1, 2\right\rangle$ onto the vector $\left\langle 4, 4, -3\right\rangle$, with steps shown.

Related calculator: Vector Projection Calculator

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Calculate the scalar projection of $\mathbf{\vec{v}} = \left\langle 5, -1, 2\right\rangle$ onto $\mathbf{\vec{u}} = \left\langle 4, 4, -3\right\rangle$.

### Solution

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

$\mathbf{\vec{v}}\cdot \mathbf{\vec{u}} = 10$ (for steps, see dot product calculator).

$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{41}$ (for steps, see vector magnitude calculator).

Thus, the scalar projection is $\frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}} = \frac{10}{\sqrt{41}} = \frac{10 \sqrt{41}}{41}.$

The scalar projection is $\frac{10 \sqrt{41}}{41}\approx 1.561737618886061$A.