Unit vector in the direction of $\left\langle \sqrt{2}, -1, 1\right\rangle$

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

The magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = 2$ (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 $\mathbf{\vec{e}} = \left\langle \frac{\sqrt{2}}{2}, - \frac{1}{2}, \frac{1}{2}\right\rangle$ (for steps, see vector scalar multiplication calculator).

The unit vector in the direction of $\left\langle \sqrt{2}, -1, 1\right\rangle$A is $\left\langle \frac{\sqrt{2}}{2}, - \frac{1}{2}, \frac{1}{2}\right\rangle\approx \left\langle 0.707106781186548, -0.5, 0.5\right\rangle.$A