$$$\frac{1}{\sqrt{5 t^{2} + 1}}\cdot \left\langle 1, 2 t, t\right\rangle$$$

Calculate $$$\frac{1}{\sqrt{5 t^{2} + 1}}\cdot \left\langle 1, 2 t, t\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{GoldenRod}\left(\frac{1}{\sqrt{5 t^{2} + 1}}\right)}\cdot \left\langle 1, 2 t, t\right\rangle = \left\langle {\color{GoldenRod}\left(\frac{1}{\sqrt{5 t^{2} + 1}}\right)}\cdot \left(1\right), {\color{GoldenRod}\left(\frac{1}{\sqrt{5 t^{2} + 1}}\right)}\cdot \left(2 t\right), {\color{GoldenRod}\left(\frac{1}{\sqrt{5 t^{2} + 1}}\right)}\cdot \left(t\right)\right\rangle = \left\langle \frac{1}{\sqrt{5 t^{2} + 1}}, \frac{2 t}{\sqrt{5 t^{2} + 1}}, \frac{t}{\sqrt{5 t^{2} + 1}}\right\rangle$$$

$$$\frac{1}{\sqrt{5 t^{2} + 1}}\cdot \left\langle 1, 2 t, t\right\rangle = \left\langle \frac{1}{\sqrt{5 t^{2} + 1}}, \frac{2 t}{\sqrt{5 t^{2} + 1}}, \frac{t}{\sqrt{5 t^{2} + 1}}\right\rangle = \left\langle \left(5 t^{2} + 1\right)^{-0.5}, \frac{2 t}{\left(5 t^{2} + 1\right)^{0.5}}, \frac{t}{\left(5 t^{2} + 1\right)^{0.5}}\right\rangle$$$A