Unit vector in the direction of $$$\left\langle \frac{6}{7}, \frac{4}{7}, - \frac{9}{7}\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle \frac{6}{7}, \frac{4}{7}, - \frac{9}{7}\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{133}}{7}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{6 \sqrt{133}}{133}, \frac{4 \sqrt{133}}{133}, - \frac{9 \sqrt{133}}{133}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle \frac{6}{7}, \frac{4}{7}, - \frac{9}{7}\right\rangle$$$A is $$$\left\langle \frac{6 \sqrt{133}}{133}, \frac{4 \sqrt{133}}{133}, - \frac{9 \sqrt{133}}{133}\right\rangle\approx \left\langle 0.520265981714472, 0.346843987809648, -0.780398972571708\right\rangle.$$$A