If P ( 3 , 2 , 6 ) is a point in space and Q is a point on the line r ˉ = ( i ^ − j ^ + 2 k ^ ) + μ ( − 3 i ^ + j ^ + 5 k ^ ) , then the value of μ for which the vector PQ is parallel to the pla

Question

If P ( 3 , 2 , 6 ) is a point in space and Q is a point on the line r ˉ = ( i ^ − j ^ ​ + 2 k ^ ) + μ ( − 3 i ^ + j ^ ​ + 5 k ^ ) , then the value of μ for which the vector PQ ​ is parallel to the plane x − 4 y + 3 z = 1 , is

TestHub · Accepted Answer

​ P ≡ 3 i ^ + 2 j ^ ​ + 6 k and Q ≡ ( 1 − 3 μ ) i ^ + ( μ − 1 ) j ^ ​ + ( 2 + 5 μ ) k ⇒ PQ ​ = ( − 2 − 3 μ ) i ^ + ( μ − 3 ) j ^ ​ + ( 5 μ − 4 ) k ^ ​ ∵ PQ ​ is parallel to the plane x − 4 y + 3 z = 1

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

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