Let a line L pass through the origin and be perpendicular to the lines L 1 : r → = i ^ - 11 j ^ - 7 k ^ + λ i ^ + 2 j ^ + 3 k ^ , λ ∈ ℝ and L 2 : r → = - i ^ + k ^ + μ 2 i ^ + 2 j ^ + k ^ , μ ∈ ℝ . If P is the point of intersection of L and L 1 , and , Q α , β , γ is the foot of perpendicular from P on L 2 , then 9 α + β + γ is equa

Step-by-step solution

Given, A line L pass through the origin and be perpendicular to the lines L 1 : r → = i ^ - 11 j ^ - 7 k ^ + λ i ^ + 2 j ^ + 3 k ^ ,   λ ∈ ℝ and L 2 : r → = - i ^ + k ^ + μ 2 i ^ + 2 j ^ + k ^ ,   μ ∈ ℝ So, direction ratio of line will be, i ^ j ^ k ^ 1 2 3 2 2 1 = i ^ - 4 - j ^ - 5 + k ^ - 2 = - 4 i ^ + 5 j ^ - 2 k ^ Hence, the equation of line L which passes through origin will be, L : r → = σ ( - 4 i ^ + 5 j ^ - 2 k ^ ) Now finding the