Question

Equation of the line passing through $(1,1,1)$ and parallel to the plane $2x+3y+z+5=0$ is

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

Answer 1

Answer: (B)

$\frac{x-1}{-1}=\frac{y-1}{1}=\frac{z-1}{-1}$

Line parallel to $2x+3y+z+5=0$ means it is perpendicular to normal to plane.
If direction cosines of line are $\alpha ,\beta$ and $\gamma$ then
$2\alpha +3\beta +\gamma =0$
It is satisfied if $\alpha =-1,\beta =1,\gamma =-1$
$\therefore$ Equation of line passing through $(1,1,1)$
having D.C's $(-1,1,-1)$ is
$\frac{x-1}{-1}=\frac{y-1}{1}=\frac{z-1}{-1}$