# Math Help - Equations of Planes

1. ## Equations of Planes

Find the scalar equation of the plane that passes through the origin and the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0

2. Originally Posted by skeske1234
Find the scalar equation of the plane that passes through the origin and the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0
Any plane that passes through the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0 can be written as:

$(3x+4y-7z-2)+\alpha(2x+3y-4)=0$ --------(1)

Since this plane passes through the origin,

$-2+\alpha(-4)=0$

$\alpha=-\frac{1}{2}$

Substituting in (1),

$(3x+4y-7z-2)-\frac{1}{2}(2x+3y-4)=0$

$6x+8y-14z-4-2x-3y+4=0$

$4x+5y-14z=0$