Question

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,2),$ then the equation of the plane is

• A. $-x+2y+8y-9=0$
• B. $x+2y+2z-9=0$
• C. $x+y+z-5=0$
• D. $x+2y-3z+1=0$

Answer 1

Answer: (B)

$x+2y+2z-9=0$

Answer 2

The correct answer is B:$x+2y+2z-9=0$
Let $A(1,2,2)$ be the foot of the perpendicular from
$O(0,0,0)$
on the plane, then direction ratio of OA are
$(1-0,\,2-0,\,2-0)$ ie, $(1,2,2)$ .
Also it passes through A.
$\therefore$ Equation of the plane is
$1(x-1)+2(y-2)+2(z-2)=0$
$\Rightarrow$ $x+2y+2z-9=0$