# How do you find a unit vector that is orthogonal to both u = (1, 0, 1) v = (0, 1, 1)?

##### 1 Answer

Jul 23, 2016

#### Explanation:

The cross product of

#(u_1, u_2, u_3) xx (v_1, v_2, v_3) = (abs((u_2, u_3),(v_2, v_3)), abs((u_3, u_1),(v_3, v_1)), abs((u_1, u_2),(v_1, v_2)))#

This will be orthogonal to both

So we find:

#u xx v = (1, 0, 1) xx (0, 1, 1)#

#= (abs((0, 1),(1, 1)), abs((1, 1),(1, 0)), abs((1, 0),(0,1)))#

#= (-1, -1, 1)#

Then:

So to make

#1/sqrt(3) (-1, -1, 1) = sqrt(3)/3 (-1, -1, 1) = (-sqrt(3)/3, -sqrt(3)/3, sqrt(3)/3)#