Question

How do you find a unit vector that is orthogonal to both 2i+2j and 2i+2k where i,j, and k are vector use dot product?

Answer 1

See below.

Explanation:

Given `vec a=(2,2,0)` and `vec b = (2,0,2)` we can argue for a vector `vec v = (v_1,v_2,v_3)` such that

`norm vec v > 0`
`<< vec a , vec v >> = 0` and
`<< vec b, vec v >> = 0` resulting in the conditions

`{(v_1^2+v_2^2+v_3^2=normv^2=1),(2v_1+2v_2=0),(2v_1+2v_3=0):}`

solving this system regarding `v_1,v_2,v_3` we obtain

`vec v = 1/sqrt(3)(-1,1,1)`