If the distance of the point P ( 1 , − 2 , 1 ) from the plane x + 2 y − 2 z = α , where α 0 , is 5 , then the foot of the perpendicular from P to the plane is

Question

If the distance of the point P ( 1 , − 2 , 1 ) from the plane x + 2 y − 2 z = α , where α > 0 , is 5 , then the foot of the perpendicular from P to the plane is

TestHub · Accepted Answer

Distance of point P from plane = 5 ∴ = ​ 3 1 − 4 − 2 − α ​ ​ α = 10 ​ Foot of perpendicular 1 x − 1 ​ ⇒ x ​ = 2 y + 2 ​ = − 2 z − 1 ​ = 3 5 ​ = 3 8 ​ , y = 3 4 ​ , z = − 3 7 ​ ​ Thus, the foot of the perpendicular is A ( 3 8 ​ , 3 4 ​ , − 3 7 ​ )

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

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