Let ₁ be the plane determined by the vectors i +2 j and 3 j -2 k . Let ₂ be the plane determined by the vectors j +2 k and 3 k -2 i . If is the angle between ₁ and ₂ , then =

Step-by-step solution

Let A ₁= i +2 j and A ₂=3 j -2 k be the vectors related to ₁ and B ₁= j -2 k , B ₂=3 k -2 i be the vectors related to ₂ Vector perpendicular to plane ₁= n ₁= A ₁ A ₂ n ₁=-4 i +2 j +3 k Vector perpendicular to plane ₂= n ₂= B ₁ B ₂ n ₂=3 i +4 j +2 k Hence angle between ₁ and ₂= angle between normals to the plane n ₁ and n ₂ aligned & = n ₁ n ₂ | n ₁ | | n ₂ | = -12-8+6 29 29 & = -14 29 aligned