Question

If the foot of the perpendicular drawn from $(0,0,0)$ to a plane is $(1,2,3)$, then the equation of the plane is

• A. $2x + y + 3z = 14$
• B. $x + 2y + 3z = 14$
• C. $x + 2y + 3z + 14 = 0$
• D. $x + 2y - 3z = 14$

Hint:

Plane from Foot of Perpendicular.
Vector from origin to foot gives normal. Use point-normal form: $a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$.

Answer 1

The Correct Option is B

Direction vector of perpendicular = $(1,2,3)$ $\rightarrow$ normal to the plane. Using point-normal form: \[ (x-1)(1) + (y-2)(2) + (z-3)(3) = 0 \Rightarrow x + 2y + 3z = 14 \]