What is the Foot of a Perpendicular Line?
If P be the foot of perpendicular, then P is (lr + x1, mr + y1, nr + z1). Find the direction ratios of AP and apply the condition of perpendicularity of AP and the given line. This will give the value of r and hence the point P, which is foot of perpendicular.
Length and equation of perpendicular:
The length of the perpendicular is the distance AP and its equation is the line joining two known points A and P.
The length of the perpendicular is the perpendicular distance of given point from that line.
Reflection or image of a point in a straight line:
If the perpendicular PL from point P on the given line be produced to Q such that PL = QL, then Q is known as the image or reflection of P in the given line. Also, L is the foot of the perpendicular or the projection of P on the line.
