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Unit vector in the direction of $$$\left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = 2$$$ (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 $$$\mathbf{\vec{e}} = \left\langle - \frac{\sin{\left(t \right)}}{2}, \frac{\sqrt{3}}{2}, \frac{\cos{\left(t \right)}}{2}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle$$$A is $$$\left\langle - \frac{\sin{\left(t \right)}}{2}, \frac{\sqrt{3}}{2}, \frac{\cos{\left(t \right)}}{2}\right\rangle\approx \left\langle - 0.5 \sin{\left(t \right)}, 0.866025403784439, 0.5 \cos{\left(t \right)}\right\rangle.$$$A