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JEE Main202224 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

Let a line having direction ratios 1 , - 4 , 2 intersect the lines x - 7 3 = y - 1 - 1 = z + 2 1 and x 2 = y - 7 3 = z 1 at the points A and B . Then A B 2 is equal to

Correct answer

0

Step-by-step solution

Let A be 3 λ + 7 , - λ + 1 , λ - 2 and B be 2 μ , 3 μ + 7 , μ DR's of A B is 3 λ - 2 μ + 7 , - λ - 3 μ - 6 , λ - μ - 2 Now, 3 λ - 2 μ + 7 1 = - λ - 3 μ - 6 - 4 = λ - μ - 2 2 i.e. - 12 λ + 8 μ - 28 = - λ - 3 μ - 6 ⇒ λ = μ - 2 Also - 2 λ - 6 μ - 12 = - 4 λ + 4 μ + 8 ⇒ λ = 5 μ + 10 After solving above two equations, we get λ = - 5 , μ = - 3 i.e.

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