Let A be a vector parallel to line of intersection of planes P₁ and P₂ through origin. P₁ is parallel to the vectors 2 j +3 k and 4 j -3 k and P₂ is parallel to j - k and 3 i +3 j , then the angle between A and 2 i + j -2 k is

Step-by-step solution

Vector equation of the plane passing through the point A( a ) and parallel to non-zero vectors b and c is r ( b c )= a ( b c ) Plane P₁ is passing through the origin and parallel to vectors b₁ =2 j +3 k and c₁ =4 j -3 k b ₁ c ₁ = | array ccc i & j & k 0 & 2 & 3 0 & 4 & -3 array |=-18 i Equation of P ₁ is: r (-18 i )=0 Plane P₂ is passing through the origin and parallel to vectors b₂ = j - k and c₂ =3 i +3 j b₂ c₂ = | array ccc i & j & k 0 & 1 & -1 3 & 3 & 0 array |=3 i -3 j -3 k Equation of P ₂ is : r ₂ (3 i -3 j -