Unit vector in the direction of $$$\left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{20 \sqrt{221} + 442}}{11}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle - \frac{11 \left(\frac{10}{11} + \frac{\sqrt{221}}{11}\right)}{\sqrt{20 \sqrt{221} + 442}}, \frac{11}{\sqrt{20 \sqrt{221} + 442}}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle$$$A is $$$\left\langle - \frac{11 \left(\frac{10}{11} + \frac{\sqrt{221}}{11}\right)}{\sqrt{20 \sqrt{221} + 442}}, \frac{11}{\sqrt{20 \sqrt{221} + 442}}\right\rangle\approx \left\langle -0.914514295677304, 0.404553584833757\right\rangle.$$$A