Let a straight line L pass through the point P ( 2 , − 1 , 3 ) and be perpendicular to the lines 2 x − 1 = 1 y + 1 = − 2 z − 3 and 1 x − 3 = 3 y − 2 = 4 z + 2 . If the line L intersects th

Question

Let a straight line L pass through the point P ( 2 , − 1 , 3 ) and be perpendicular to the lines 2 x − 1 ​ = 1 y + 1 ​ = − 2 z − 3 ​ and 1 x − 3 ​ = 3 y − 2 ​ = 4 z + 2 ​ . If the line L intersects the yz -plane at the point Q , then the distance between the points P and Q is :

TestHub · Accepted Answer

Vector parallel to L ​ = ​ i ^ 2 1 ​ j ^ ​ 1 3 ​ k ^ − 2 4 ​ ​ = 10 i ^ − 10 j ^ ​ + 5 k ^ = 5 ( 2 i ^ − 2 j ^ ​ + k ^ ) ​ Equation of ' L ' 2 x − 2 ​ = − 2 y + 1 ​ = 1 z − 3 ​ = λ ( say ) Let Q ( 2 λ + 2 , − 2 λ − 1 , λ + 3 ) ​ ⇒ 2 λ + 2 = 0 ⇒ λ = − 1 ⇒ Q ( 0 , 1 , 2 ) d ( P , Q ) = 3 ​

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