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