Gives the line L : 3 x − 1 = 2 y + 1 = − 1 z − 3 and the plane π : x − 2 y − z = 0 . Of the following assertions, the only one that is always true is

Question

Gives the line L : 3 x − 1 ​ = 2 y + 1 ​ = − 1 z − 3 ​ and the plane π : x − 2 y − z = 0 . Of the following assertions, the only one that is always true is

TestHub · Accepted Answer

Since 3 ( 1 ) + 2 ( − 2 ) + ( − 1 ) ( − 1 ) = 3 − 4 + 1 = 0 ∴ Given line is ⊥ to the normal to the plane i.e., given line is parallel to the given plane. Also, ( 1 , − 1 , 3 ) lies on the plane x − 2 y − z = 0 if 1 − 2 ( − 1 ) − 3 = 0 i.e., 1 + 2 − 3 = 0 which is true ∴ L lies in plane π .

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

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