# Thread: Convert from plane equation to scalar equation

1. ## Convert from plane equation to scalar equation

1. The problem statement, all variables and given/known data
When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0?
I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.

2. Originally Posted by TN17
1. The problem statement, all variables and given/known data
When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0?
I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.
1. The vectors $\displaystyle \vec r, \vec a, \vec b$ consist of 3 components.

2. You can re-arrange the given equation of a plane into a system of 3 simultaneous equations:

$\displaystyle \left|\begin{array}{l}x = r_1+s \cdot a_1 + t \cdot b_1 \\ y = r_2+s \cdot a_2 + t \cdot b_2 \\ z=r_3+s \cdot a_3 + t \cdot b_3 \end{array}\right.$

3. Use the first two equation to solve for s and t and plug in these terms into the 3rd equation. Simplify and collect like terms.