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

Answer: (D)

Equation of the plane will be
$\left|\begin{array}{ccc}x-1& y-2& z+3\\ 2-1& -2-2& 1-(-3)\\ 1& 0& 0\end{array}\right|=0$
$\Rightarrow \left|\begin{array}{ccc}x-1& y-2& z+3\\ 1& -4& 4\\ 1& 0& 0\end{array}\right|=0$
$\Rightarrow 1[4(y-2)+4(z+3)]=0$
[Expanding along $R_3$ ]
$\Rightarrow 4y-8+4z+12=0$
$\Rightarrow 4y+4z+4=0$
$\Rightarrow y+z+1=0$