# 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]

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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