Let a → be a non-zero vector parallel to the line of intersection of the two planes described by i ^ + j ^ , i ^ + k ^ and i ^ - j ^ , j ^ - k ^ . If θ is the angle between the vector a → and the vector b → = 2 i ^ - 2 j ^ + k ^ and a → · b → = 6 , then the ordered pair θ , | a → × b → | is equal to

Step-by-step solution

Given, a → be a non-zero vector parallel to the line of intersection of the two planes described by i ^ + j ^ , i ^ + k ^ , So finding the normal vector to the above plane, we get, n → 1 = i ^ j ^ k ^ 1 1 0 1 0 1 = i ^ - j ^ - k ^ And normal vector to planes i ^ - j ^ , j ^ - k ^ will be, n → 2 = i ^ j ^ k ^ 1 - 1 0 0 1 - 1 = i ^ + j ^ + k ^ Now a → = λ n → 1 × n → 2 So, direction ratio of a → = i ^ j ^ k ^ 1 - 1 - 1 1 1 1 = - 2 j ^ + 2 k ^ Hence, direction ratio