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Question
If the straight lines `(x - 5)/(5"m" + 2) = (2 - y)/5 = (1 - z)/(-1)` and x = `(2y + 1)/(4"m") = (1 - z)/(-3)` are perpendicular to ech other find the value of m
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Solution
`(x - 5)/(5"m" + 2) = (2 - y)/5 = (1 - z)/(-1)` and x = `(2y + 1)/(4"m") = (1 - z)/(-3)` are perpendicular
Rewrite the above equations
`(x - 5)/(5"m" + 2) = (y - 2)/(-5) = (z - 1)/1` and `(y + 1/2)/(2"m") = (z - 1)/3`
So, we get, `vec"b" = (5"m" + 2)vec"i" - 5vec"j" + vec"k"`
`vec"d" = vec"i" + 2"m"vec"j" + 3vec"k"`
`vec"b" * vec"d"` = 0 ......(Given)
5m + 2 – 10m + 3 = 0
– 5m = – 5
⇒ – 5m + 5 = 0
⇒ m = 1
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