Question

The equation of the plane passing through the origin and containing the lines whose d.cs are proportional to $1,-2,2$ and $2,3,-1$ is:

• A. $x-2y+2z=0$
• B. $2x+3y-z=0$
• C. $x+5y-3z=0$
• D. $4x-5y-7z=0$

Answer 1

The correct option is D $4x-5y-7z=0$

Equation of plane passing through origin is given by,
$ax+by+cz=0$
Also this line containing line whose d.cs are $(1,-2,2)$ and $(2,3,-1)$
$\Rightarrow a-2b+2c=0$ and $2a+3b-c=0$
Solving these, $b=\frac{5c}{7},a=-\frac{4c}{7}$
Hence, plane equation is
$4x-5y-7z=0$