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

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

Multiply each coordinate of the vector by the scalar:

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

$\frac{1}{2}\cdot \left\langle \sqrt{2}, -1, 1\right\rangle = \left\langle \frac{\sqrt{2}}{2}, - \frac{1}{2}, \frac{1}{2}\right\rangle\approx \left\langle 0.707106781186548, -0.5, 0.5\right\rangle$A