How Do You Find a Scalar Equation for a Plane Through Three Points?

[Hollysmoke]

The question is,

Find a scalar equation that passes through the points (3,2,3), (-4,1,2) and (-1,3,2).

What I did was put that into the vector equation form, using (3,2,3) as a position vector, resulting in:

r=(3,2,3) +t(-7,-1,-1) + s(-5,2,0)

Then I found the cross product of the directional vectors and went from there, but my final answer was different then the one in the textbook. Can someone tell me what I did wrong please?

 

[0rthodontist]

s should be multiplied by (-3, 2, 0). Looks like you added instead of subtracted.

The better way to do this problem is to solve the system of equations, with matrix algebra if you have it.

 

[HallsofIvy]

I have no idea what it means for an "equation" to pass through three points. A line or a plane can pass through points but an equation is not a geometric object and has nothing to do with "points".