Question

In the following case, find the coordinates of the foot of the perpendicular drawn from the origin:

5y +8 =0

Answer 1

Given plane is 0x +5y +0z +8= 0 ....(v)

Dr's of any line perpendicular to plane (v) are 0,5,0.

Hence, equation of the line through origin and at right angle to plane (v) are

$\frac{x-0}{0}=\frac{y-0}{5}=\frac{z-0}{0}$ ...(vi)

Any point on this line is (0,5t,0). This lies in plane (v) if $5\times 5t+8=0$ i.e., $t=\frac{-8}{25}$

Hence, the required foot of perpendicular is $(0,5(-\frac{8}{25}),0)(0,\frac{8}{25},0)$