$$$\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\cdot \left\langle 4 t^{3}, - \sin{\left(t \right)}, 3\right\rangle$$$

Calculate $$$\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\cdot \left\langle 4 t^{3}, - \sin{\left(t \right)}, 3\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{Red}\left(\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right)}\cdot \left\langle 4 t^{3}, - \sin{\left(t \right)}, 3\right\rangle = \left\langle {\color{Red}\left(\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right)}\cdot \left(4 t^{3}\right), {\color{Red}\left(\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right)}\cdot \left(- \sin{\left(t \right)}\right), {\color{Red}\left(\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right)}\cdot \left(3\right)\right\rangle = \left\langle \frac{4 t^{3}}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}, - \frac{\sin{\left(t \right)}}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}, \frac{3}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right\rangle$$$

$$$\frac{1}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\cdot \left\langle 4 t^{3}, - \sin{\left(t \right)}, 3\right\rangle = \left\langle \frac{4 t^{3}}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}, - \frac{\sin{\left(t \right)}}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}, \frac{3}{\sqrt{16 t^{6} + \sin^{2}{\left(t \right)} + 9}}\right\rangle = \left\langle \frac{t^{3}}{\left(t^{6} + 0.0625 \sin^{2}{\left(t \right)} + 0.5625\right)^{0.5}}, - \frac{0.25 \sin{\left(t \right)}}{\left(t^{6} + 0.0625 \sin^{2}{\left(t \right)} + 0.5625\right)^{0.5}}, \frac{0.75}{\left(t^{6} + 0.0625 \sin^{2}{\left(t \right)} + 0.5625\right)^{0.5}}\right\rangle$$$A