The vectors A B =3 i -2 j +2 k and B C = i -2 k are the adjacent sides of a parallelogram. The angle between its diagonals is

Step-by-step solution

Given, A B =3 i -2 j +2 k and B C = i -2 k aligned Diagonals A C & = A B + B C & =3 i -2 j +2 k + i -2 k & =4 i -2 j aligned and aligned B D & = B C - A B & = i -2 k -(3 i -2 j +2 k ) & =-2 i +2 j -4 k aligned = A C B D | A C || B D | aligned & = (4 i -2 j ) (-2 i +2 j -4 k ) 4^2+(-2)^2 (-2)^2+(2)^2+(-4)^2 & = -8-4 20 24 =- 12 4 30 =- 3 30 =- 3 10 & = ⁻¹ (- 3 10 ) & or - ⁻¹ (- 3 10 ) & aligned