Question

The equation of the plane perpendicular to the $z$-axis and passing through $(2,-3,5)$ is

• A. $x-2=0$
• B. $y+3=0$
• C. $z-5=0$
• D. $2x-3y+5z+4=0$

Answer 1

Answer: (C)

$z-5=0$

Answer 2

Since, the plane perpendicular to z-axis, so the normal of the plane is parallel to z-axis, the direction cosine's of z-axis is $(0,0,1)$ . Then, the equation of plane which passes through the point $(3,-3,5)$ and perpendicular to z-axis is
$0(x-2)+0(y+3)+1(z-5)=0$ $\Rightarrow$ $z-5=0$