Q. 294.3( 3 Votes )

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector to the plane Also find image of P in the plane.[CBSE 2016]

Answer :



To find: position vector of the foot of perpendicular and the perpendicular distance from the point P to given plane and the image of P in the plane.


Formula used:









Therefore,


















Hence, position vector of the foot of perpendicular and the perpendicular distance from the point P to given plane are



Let Q be the image of the point P to the given plane


PQ will be normal to the plane


Therefore, equation of PQ is



As Q lies on line PQ, the position vector of Q is




Let R is mid-point of PQ. Position vector of R is





R will also lie on the plane.













Put the value of λ = 1:




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