Find the Value of λ for Which the Following Lines Are Perpendicular to Each Other X − 5 5 λ + 2 = 2 − Y 5 = 1 − Z − 1 ; X 1 = Y + 1 2 2 λ = Z − 1 3 Hence, Find Whether the Lines Intersect Or Not - Mathematics

Question

Sum

Find the value of λ for which the following lines are perpendicular to each other ("x"-5)/(5λ+2) = (2 -"y")/(5) = (1 -"z")/(-1); ("x")/(1) = ("y"+1/2)/(2λ) = ("z" -1)/(3)

hence, find whether the lines intersect or not

Solution

("x"-5)/(5λ+2) = ("y"-2)/(-5) = ("z"-1)/(1)                      ....(1)

and

("x")/(1) = ("y"+1/2)/(2λ) = ("z" -1)/(3)                              ...(2)

a1 = 5λ + 2, b1 = -5, c1 = 1 and

a2 = 1, b2 = 2λ, c2 = 3

a1a2 + b1b2 + c1c2 = 0

(5λ + 2) - 5(2λ) + 1(3) = 0

-5λ + 5 = 0

⇒ λ = -1

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