Find two unit vectors orthogonal to a=⟨2,−2,−3⟩a=⟨2,−2,−3⟩ and b=⟨3,2,2⟩b=⟨3,2,2⟩ enter your answer so that the first non-zero coordinate of the first vector is positive.
We need the cross product of the two vectors. a x b =<2,-2,-3> x <3,2,2> = i j k 2 -2 -3 3 2 2 =<-4+6, -(4+9), 4+6> =<2,-13,10> The second vector is obtained by reversing the direction, namely <-2,13,-10> Thus the two vectors are <2,-13,10> and <-2,13,-10>.
