Answer:
[tex](-\frac{- \sqrt{3}}{3},-\frac{\sqrt{3}}{3} , \frac{\sqrt{3}}{3})[/tex]
Step-by-step explanation:
take u = [1,1,0] and
v = [1,0,1]
calculate the cross product of u and v
u × v = [1,1,0] × [1,0,1]
[tex][\begin{vmatrix}0 & 1\\ 1 &1\end{vmatrix}\begin{vmatrix}1 & 1\\ 1 & 0\end{vmatrix}\begin{vmatrix}1 & 0\\ 0 & 1 \end{vmatrix} ][/tex]
= (-1,-1,1)
then
[tex]\left \| -1,-1,1 \right \| = \sqrt{ -1^2 + -1^2 +1}= \sqrt{3}[/tex]
[tex]\frac{1}{\sqrt{3}}(-1,-1,1 )[/tex] to unit vector by dividing by[tex] \sqrt{3}[/tex]
[tex]\frac{\frac{1}{\sqrt{3}}(-1,-1,1 )}{\sqrt{3}} = (-\frac{- \sqrt{3}}{3},-\frac{\sqrt{3}}{3} , \frac{\sqrt{3}}{3})[/tex]
