$$$3\cdot \left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$

Calculate $$$3\cdot \left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{Peru}\left(3\right)}\cdot \left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle = \left\langle {\color{Peru}\left(3\right)}\cdot \left(- \frac{\sin{\left(t \right)}}{3}\right), {\color{Peru}\left(3\right)}\cdot \left(- \frac{\cos{\left(t \right)}}{3}\right), {\color{Peru}\left(3\right)}\cdot \left(0\right)\right\rangle = \left\langle - \sin{\left(t \right)}, - \cos{\left(t \right)}, 0\right\rangle$$$

$$$3\cdot \left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle = \left\langle - \sin{\left(t \right)}, - \cos{\left(t \right)}, 0\right\rangle$$$A