Statement 1 - The line 3 x − 2 = 4 y − 3 = 5 z − 4 is parallel to the plane 2 x + y − 2 z = 0 . Statement 2 - The normal of the given plane is perpendicular to the given line.

Question

Statement 1 - The line 3 x − 2 ​ = 4 y − 3 ​ = 5 z − 4 ​ is parallel to the plane 2 x + y − 2 z = 0 . Statement 2 - The normal of the given plane is perpendicular to the given line.

TestHub · Accepted Answer

The normal of the plane is ( 2 , 1 , − 2 ) and the direction of the line is ( 3 , 4 , 5 ) .2 ⋅ 3 + 1 ⋅ 4 − 2 ⋅ 5 = 0 , so the line is perpendicular to the normal. The point ( 2 , 3 , 4 ) gives 4 + 3 − 8  = 0 , so the line is not in the plane and is parallel to it. Both statements are true and Statement 2 explains Statement 1.

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

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