$$$\frac{\sqrt{2}}{2}\cdot \left\langle -1, 1\right\rangle$$$

Calculate $$$\frac{\sqrt{2}}{2}\cdot \left\langle -1, 1\right\rangle$$$.

Multiply each coordinate of the vector by the scalar:

$$${\color{Magenta}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left\langle -1, 1\right\rangle = \left\langle {\color{Magenta}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(-1\right), {\color{Magenta}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right)\right\rangle = \left\langle - \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right\rangle$$$

$$$\frac{\sqrt{2}}{2}\cdot \left\langle -1, 1\right\rangle = \left\langle - \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right\rangle\approx \left\langle -0.707106781186548, 0.707106781186548\right\rangle$$$A