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Unit vector in the direction of $$$\left\langle \frac{1}{5}, - \frac{3}{5}, - \frac{1}{5}, \frac{2}{5}\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle \frac{1}{5}, - \frac{3}{5}, - \frac{1}{5}, \frac{2}{5}\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{15}}{5}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{\sqrt{15}}{15}, - \frac{\sqrt{15}}{5}, - \frac{\sqrt{15}}{15}, \frac{2 \sqrt{15}}{15}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle \frac{1}{5}, - \frac{3}{5}, - \frac{1}{5}, \frac{2}{5}\right\rangle$$$A is $$$\left\langle \frac{\sqrt{15}}{15}, - \frac{\sqrt{15}}{5}, - \frac{\sqrt{15}}{15}, \frac{2 \sqrt{15}}{15}\right\rangle\approx \left\langle 0.258198889747161, -0.774596669241483, -0.258198889747161, 0.516397779494322\right\rangle.$$$A