Question

from a point p(1,2,4), a perpendicular is drawn on the plane 2x+y-2z+3=0 fond the equation , the length and coordinates of the foot of the perpendicular​

Answer 1

Given equation is 2x+y-2z+3=0

Direction ratio of normal are 2,1,-2

given point is (1,2,4)

therefore equaation will be

(x-1)/2=(y-2)/1=(z+2)/4=k (say)

any coordinate is of the fomr [2k+1,k+2,4-2k]

hence

[2(2k+1)+k+2-2(4-2k)]=

on solving this we get

9k-1=0 or k=1/9

therefore coordinate of foot of perpendicular will be (11/9,19/9,34/9)

length of perpendicular will be =1/3 units

hope it helps ❤️