Question

In the space the equation $by+cz+d=0$ represents a plane perpendicular to the plane:

• A. $YOZ$
• B. $ZOX$
• C. $XOY$
• D. $Z=k$

Answer 1

The correct option is A $YOZ$

Consider $P:bx+cz+d=0$
a) Equation of $YOZ$ plane is $x=0$
Since, $\left(i\right).(bj+ck)=0$
Therefore, $P$ is perpendicular to $YOZ$
b) Equation of $ZOX$ plane is $y=0$
Since, $\left(j\right).(bj+ck)=b\ne 0$
Therefore, $P$ is not perpendicular to $ZOX$
c) Equation of $XOY$ plane is $z=0$
Since, $\left(k\right).(bj+ck)=c\ne 0$
Therefore, $P$ is not perpendicular to $XOY$
d) Consider. $z=k$
Since, $\left(k\right).(bj+ck)=c\ne 0$
Therefore, $P$ is not perpendicular to $z=k$
Ans: A