Q58 / 160 · AP EAMCET 2012 · Mathematics

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

A
$2 x+y+3 z=14$
Correct answer
B
$x+2 y+3 z=14$
C
$x+2 y+3 z+14=0$
D
$x+2 y-3 z=14$

Solution

The equation of a plane passing through $(1,2,3)$ is $a(x-1)+b(y-2)+c(z-3)=0$ $\begin{aligned} & \text { Also, }(a, b, c)=(1-0,2-0,3-0) \\ & -(1,2,3) \\ & \therefore 1(x-1)+2(y-2)+3(z-3)=0 \\ & \Rightarrow \quad x+2 y+3 z-1-4-9=0 \\ & \Rightarrow \quad x+2 y+3 z=14 \\ & \end{aligned}$

Hence, the correct answer is option: 'B'.

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