. Image of a Point in a Plane Let A be the given point whose position vector is u . Let r n be the equation of the plane. Let v be the position vector of the mirror image A ′ of A in the plane.
Then ' AA is perpendicular to the plane. So it is parallel to n . Then AA ′ = or v u ⇒ v u ... ( ) Let M be the middle point of AA ′ .
Then the position vector of M is u v . But M lies on the plane. So, u v ⋅ ... ( ) Sustituting ( ) in ( ), we get u u ⋅ ⇒ u Therefore, the position vector of A ′ is [ )] u n v u Note The mid point of M of AA ′ is the foot of the perpendicular from the point A to the plane r n .
So the position vector of the foot M of the perpendicular is given by . u v u u u n Fig. . M ( ) A u r n ( ) A v ′ Vector - -