|
|
|
|
|
|
|
|
|
|
|
|
Unit vector in the direction of $$$\left\langle -1, \frac{3}{11}, - \frac{5}{11}, 1, 0\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle -1, \frac{3}{11}, - \frac{5}{11}, 1, 0\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{2 \sqrt{69}}{11}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle - \frac{11 \sqrt{69}}{138}, \frac{\sqrt{69}}{46}, - \frac{5 \sqrt{69}}{138}, \frac{11 \sqrt{69}}{138}, 0\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle -1, \frac{3}{11}, - \frac{5}{11}, 1, 0\right\rangle$$$A is $$$\left\langle - \frac{11 \sqrt{69}}{138}, \frac{\sqrt{69}}{46}, - \frac{5 \sqrt{69}}{138}, \frac{11 \sqrt{69}}{138}, 0\right\rangle\approx \left\langle -0.662122191971731, 0.180578779628654, -0.300964632714423, 0.662122191971731, 0\right\rangle.$$$A