Question

The equation of the plane containing the lines $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3}$ and $\frac{x}{2}=\frac{y-2}{-1}=\frac{z+1}{3}$ is

• A. $8x-y+5z-8=0$
• B. $8x+y-5z-7=0$
• C. $x-8y+3z+6=0$
• D. $8x+y-5z+7=0$

Answer 1

Answer: (B)

$8x+y-5z-7=0$

Answer 2

The equation of plane containing the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3}$ and $\frac{x}{2}=\frac{y-2}{-1}=\frac{x+1}{3}$ The required equation is $\left| \begin{matrix} x-1 & (y+1) & 3 \\\ x & y-2 & 3+1 \\\ 2 & -1 & 3 \\\ \end{matrix} \right|=0$ $\Rightarrow$ $(x-1)(3y-6+z-1)-(y+1)$ $(3x-2z-2)+z(-x-2y+4)=0$ $-5x-3y-z+5+2y-3x+2z+2+4z=0$ $\Rightarrow$ $-8x-y+5z+7=0$ $\Rightarrow$ $8x+y-5z-7=0$