Unit vector in the direction of $$$\left\langle 1, 2, -1, 0, 4\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle 1, 2, -1, 0, 4\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{22}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{\sqrt{22}}{22}, \frac{\sqrt{22}}{11}, - \frac{\sqrt{22}}{22}, 0, \frac{2 \sqrt{22}}{11}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle 1, 2, -1, 0, 4\right\rangle$$$A is $$$\left\langle \frac{\sqrt{22}}{22}, \frac{\sqrt{22}}{11}, - \frac{\sqrt{22}}{22}, 0, \frac{2 \sqrt{22}}{11}\right\rangle\approx \left\langle 0.21320071635561, 0.426401432711221, -0.21320071635561, 0, 0.852802865422442\right\rangle.$$$A