Question

The equation of the plane which is parallel to $x-y-plane$ and cuts intercept of length $3$ from the $z-axis$ is

• A. $x=3$
• B. $y=3$
• C. $z=3$
• D. $x+y+z=3$

Answer 1

The correct option is C $z=3$

Direction cosine of plane is $\perp$ to x-y plane

ie (0, 0, 1)

It also passes through (0, 0,3)

$E{q}^n$ of plane $(\overrightarrow{r}-\overrightarrow{a}).\overrightarrow{n}=0$

$\Rightarrow \overrightarrow{r}\overrightarrow{n}=\overrightarrow{a}.\overrightarrow{n}$

$\Rightarrow (x,y,z)(0,0,1)=(0,0,1)(0,0,3)$

$\Rightarrow z=3$

$\Rightarrow$ Option c is correct