Let P 1,2 , 3 be a point in space and Q be a point on the line x - 1 2 = y - 3 5 = z - 1 3 such that P Q is parallel to 5 x - 4 y + 3 z = 1 . If the length of P Q is equal to k units, then the value of k 2 is equal to

Question

Let P 1,2 , 3 be a point in space and Q be a point on the line x - 1 2 = y - 3 5 = z - 1 3 such that P Q is parallel to 5 x - 4 y + 3 z = 1 . If the length of P Q is equal to k units, then the value of k 2 is equal to,

MARKS App · Accepted Answer

Given, P 1,2 , 3 Any general point on the line is Q 2 λ + 1,5 λ + 3,3 λ + 1 P Q → = 2 λ i ^ + 5 λ + 1 j ^ + 3 λ - 2 k ^ Since, P Q → is parallel to the given plane, therefore 10 λ - 20 λ - 4 + 9 λ - 6 = 0 ⇒ - λ - 10 = 0 ⇒ λ = - 1 0 Hence, the length of P Q = 400 + 2401 + 1024 = 3825

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