Answer:
u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩
u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩
Step-by-step explanation:
for a=⟨−2,−4,−2⟩ and b=⟨−3,5,2⟩
a vector orthogonal to a and b can be found through the vectorial product of a and b. Thus
c= a x b
then c₁=⟨2,−10,−22⟩ and c₂= - c₁= ⟨-2,10,22⟩ are orthogonal to a and b
the corresponding unit vectors are
u₁=c₁/|c₁| = ⟨2,−10,−22⟩ / √(2²+(−10)²+(−22)²) = ⟨2,−10,−22⟩/(14*√3) = ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩
then u₂= - u₁= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩
then the unit vectors are
u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩
u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩