$$$\frac{11}{\sqrt{20 \sqrt{221} + 442}}\cdot \left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle$$$

Calculate $$$\frac{11}{\sqrt{20 \sqrt{221} + 442}}\cdot \left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{Purple}\left(\frac{11}{\sqrt{20 \sqrt{221} + 442}}\right)}\cdot \left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle = \left\langle {\color{Purple}\left(\frac{11}{\sqrt{20 \sqrt{221} + 442}}\right)}\cdot \left(- \frac{\sqrt{221}}{11} - \frac{10}{11}\right), {\color{Purple}\left(\frac{11}{\sqrt{20 \sqrt{221} + 442}}\right)}\cdot \left(1\right)\right\rangle = \left\langle - \frac{11 \left(\frac{10}{11} + \frac{\sqrt{221}}{11}\right)}{\sqrt{20 \sqrt{221} + 442}}, \frac{11}{\sqrt{20 \sqrt{221} + 442}}\right\rangle$$$

$$$\frac{11}{\sqrt{20 \sqrt{221} + 442}}\cdot \left\langle - \frac{\sqrt{221}}{11} - \frac{10}{11}, 1\right\rangle = \left\langle - \frac{11 \left(\frac{10}{11} + \frac{\sqrt{221}}{11}\right)}{\sqrt{20 \sqrt{221} + 442}}, \frac{11}{\sqrt{20 \sqrt{221} + 442}}\right\rangle\approx \left\langle -0.914514295677304, 0.404553584833757\right\rangle$$$A