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
$\begin{vmatrix} x-1 & y-2 & z+3 \\ 2-1 & -2-2 & 1-(-3) \\ 1 & 0 & 0\end{vmatrix}=0$
$\Rightarrow \begin{vmatrix} x-1 & y-2 & z+3 \\ 1 & -4 & 4 \\ 1 & 0 & 0\end{vmatrix}=0$
$\Rightarrow 1[4(y-2)+4(z+3)]=0$
[Expanding along $R _{3}$ ]
$\Rightarrow 4 y-8+4 z+12=0 $
$ \Rightarrow 4 y+4 z+4=0$
$\Rightarrow y+z+1=0$