Question

The equation of line passing through point $(1,-2,-1)$ and parallel to the line $2x+y=3$ and $y+z=1,$ is

• A. $\frac{x-1}{1}=\frac{y+2}{-1}=\frac{z+1}{-3}$
• B. $\frac{x-1}{-2}=\frac{y+2}{-1}=\frac{z+1}{3}$
• C. $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z+1}{2}$
• D. $\frac{x-1}{-2}=\frac{y+2}{-1}=\frac{z+1}{1}$

Answer 1

The correct option is C $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z+1}{2}$

GIven line : $2x+y=3$ and $y+z=1$
$\Rightarrow 2x-2=1-y$ and $1-y=z$
So, equation of line is $2x-2=1-y=z$
$\Rightarrow \frac{x-1}{1/2}=\frac{y-1}{-1}=\frac{z-0}{1}\Rightarrow \frac{x-1}{1}=\frac{y-1}{-2}=\frac{z}{2}$
$\Rightarrow$ d.r's of line : $(a,b,c)=(1,-2,2)$
So, equation of line passing through $(1,-2,-1)$ and parallel to above line is given by :
$\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z+1}{2}$