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Question
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
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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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