The coordinates of the foot of the perpendicular drawn from the origin to the plane $2 x+y-2 z=18$ are
The coordinates of the foot of the perpendicular drawn from the origin to the plane $2 x+y-2 z=18$ are
$(4,2,-4)$
$(1,2,-3)$
$(4,2,4)$
$(4,-2,-4)$
Solution
$2 x+y-2 z=18$
Dividing both sides $\sqrt{(2)^2+(1)^2+(-2)^2}=3$, we get
$\left(\frac{2}{3}\right) \mathrm{x}+\left(\frac{1}{3}\right) \mathrm{y}-\left(\frac{2}{3}\right) \mathrm{z}=6$
Hence length of perpendicular from origin to the plane is 6 . Therefore coordinates of foot of perpendicular are $\left[\left(\frac{2}{3}\right)(6),\left(\frac{1}{3}\right)(6),\left(\frac{-2}{3}\right)(6)\right]$ i.e. $(4,2,-4)$