Question

The equation of the plane through $(1,2,-3)$ and $(2,-2,1)$ and parallel to $X-$ axis is

• A. $y-z+1=0$
• B. $y-z-1=0$
• C. $y+z-1=0$
• D. $y+z+1=0$

Answer 1

The correct option is D $y+z+1=0$

Suppose direction ratio of plane are $(l,m,n)$
Given plane is parallel to $X-$axis
$\therefore l+0\cdot m+0\cdot n=0\Rightarrow l=0$
As direction ratio is $(0,m,n)$
Direction ratio of the line joining the points
$(1,2,-3)\&(2,-2,1)=(1,-4,4)$

$\therefore 0\cdot \left(1\right)+m(-4)+n\left(4\right)=0\Rightarrow -4m+4n=0\Rightarrow m=n$
Therefore equation of plane
$0\cdot (x-1)+m\cdot (y-2)+n\cdot (z+3)=0\Rightarrow y-2+z+3=0\Rightarrow y+z+1=0$