Unit vector in the direction of $\left\langle 1, 2, 1\right\rangle$

Find the unit vector in the direction of $\mathbf{\vec{u}} = \left\langle 1, 2, 1\right\rangle$.

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

The unit vector is obtained by dividing each coordinate of the given vector by the magnitude.

Thus, the unit vector is $\mathbf{\vec{e}} = \left\langle \frac{\sqrt{6}}{6}, \frac{\sqrt{6}}{3}, \frac{\sqrt{6}}{6}\right\rangle$ (for steps, see vector scalar multiplication calculator).

The unit vector in the direction of $\left\langle 1, 2, 1\right\rangle$A is $\left\langle \frac{\sqrt{6}}{6}, \frac{\sqrt{6}}{3}, \frac{\sqrt{6}}{6}\right\rangle\approx \left\langle 0.408248290463863, 0.816496580927726, 0.408248290463863\right\rangle.$A