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
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)#