A plane through P = ( 0 , 1 , − 1 ) contains line L : 2 x − 1 = 3 y − 1 = 1 z + 2 . Point R lies on L and △ PQR is right-angled at P , where Q = ( 1 , 1 , − 2 ) . Find P R 2 /5 .

Question

A plane through P = ( 0 , 1 , − 1 ) contains line L : 2 x − 1 ​ = 3 y − 1 ​ = 1 z + 2 ​ . Point R lies on L and △ PQR is right-angled at P , where Q = ( 1 , 1 , − 2 ) . Find P R 2 /5 .

TestHub · Accepted Answer

Put R = ( 2 t + 1 , 3 t + 1 , t − 2 ) . From PR ⋅ PQ ​ = 0 , t = − 2 , so P R 2 = 54 and P R 2 /5 = 10.8 .

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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