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)

$y + z + 1 = 0$

Answer 2

The correct answer is D:$y+z+1=0$
The points are: $(1,2,-3)$ and $(2,-2,1)$ and parallel to x-axis
Equation of the plane will be
$\begin{vmatrix} x-1 & y-2 & z+3 \\\ 2-1 & -2-2 & 1-(-3) \\\ 1 & 0 & 0\end{vmatrix}=0$
$\Rightarrow \begin{vmatrix} x-1 & y-2 & z+3 \\\ 1 & -4 & 4 \\\ 1 & 0 & 0\end{vmatrix}=0$
$\Rightarrow 1[4(y-2)+4(z+3)]=0$
$\Rightarrow 4 y-8+4 z+12=0$
$\Rightarrow 4 y+4 z+4=0$
$\Rightarrow y+z+1=0$