Unit vector in the direction of $$$\left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = 3$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{\cos{\left(t \right)}}{3}, - \frac{\sin{\left(t \right)}}{3}, \frac{2 \sqrt{2}}{3}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle$$$A is $$$\left\langle \frac{\cos{\left(t \right)}}{3}, - \frac{\sin{\left(t \right)}}{3}, \frac{2 \sqrt{2}}{3}\right\rangle\approx \left\langle 0.333333333333333 \cos{\left(t \right)}, - 0.333333333333333 \sin{\left(t \right)}, 0.942809041582063\right\rangle.$$$A