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?

1 Answer
Cesareo R.
Sep 18, 2016

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)

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