A line from the origin meets the lines 1 x − 2 = − 2 y − 1 = 1 z + 1 and 2 x − 8/3 = − 1 y + 3 = 1 z − 1 at P and Q respectively. If the distance PQ = l then the value of [ l ] (where [.]

Question

A line from the origin meets the lines 1 x − 2 ​ = − 2 y − 1 ​ = 1 z + 1 ​ and 2 x − 8/3 ​ = − 1 y + 3 ​ = 1 z − 1 ​ at P and Q respectively. If the distance PQ = l then the value of [ l ] (where [.] represents the greatest integer function), is

TestHub · Accepted Answer

From the given conditions, we have, λ + 2 2 μ + 8/3 ​ = 2 λ − 1 μ + 3 ​ = λ − 1 μ + 1 ​ ⇒ λ = 3 , μ = 3 1 ​ ⇒ P ≡ ( 5 , − 5 , 2 ) Q ≡ ( 3 10 ​ , 3 − 10 ​ , 3 4 ​ ) ⇒ l = PQ = 6 ​ ⇒ [ l ] = 2

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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