$$$\frac{1}{3}\cdot \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle$$$

Calculate $$$\frac{1}{3}\cdot \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{Chartreuse}\left(\frac{1}{3}\right)}\cdot \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle = \left\langle {\color{Chartreuse}\left(\frac{1}{3}\right)}\cdot \left(\cos{\left(t \right)}\right), {\color{Chartreuse}\left(\frac{1}{3}\right)}\cdot \left(- \sin{\left(t \right)}\right), {\color{Chartreuse}\left(\frac{1}{3}\right)}\cdot \left(2 \sqrt{2}\right)\right\rangle = \left\langle \frac{\cos{\left(t \right)}}{3}, - \frac{\sin{\left(t \right)}}{3}, \frac{2 \sqrt{2}}{3}\right\rangle$$$

$$$\frac{1}{3}\cdot \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 2 \sqrt{2}\right\rangle = \left\langle \frac{\cos{\left(t \right)}}{3}, - \frac{\sin{\left(t \right)}}{3}, \frac{2 \sqrt{2}}{3}\right\rangle\approx \left\langle 0.333333333333333 \cos{\left(t \right)}, - 0.333333333333333 \sin{\left(t \right)}, 0.942809041582063\right\rangle$$$A