Question

General equation of a plane which is parallel to x-axis is

• A. $ax+by+cz+d=0,a\ne 0,b\ne 0,c\ne 0$.
• B. $ax+by+d=0,a\ne 0,b\ne 0$
• C. $by+cz+d=0,b\ne 0,c\ne 0$
• D. $ax+cz+d=0,a\ne ,b\ne 0$

Answer 1

The correct option is C $by+cz+d=0,b\ne 0,c\ne 0$

Equation of $x$-axis in $\frac{x}{l}=\frac{y}{0}=\frac{z}{0}$.
Let the equation of the plane parallel to $x$-axis be $ax+by+cz+d=0$
Since the normal to the plane in perpendicular to $x$-axis.
$al+b\times 0+c\times 0=0\Rightarrow a=0$
So that required equation is
$by+cz+d=0$ where $b\ne 0,c\ne 0$.