How Do You Find the Scalar Equation of a Plane from Two Points and a Vector?

[agenttiny200]

Homework Statement

Find the scalar equation of the plane containing the points A(-3, 1, 1) and B(-4, 0, 3) and the vector u = [1, 2, 3].

Homework Equations

I am at a lost, since I can't tell how to figure out the normal vector. I am supposed to find:
Ax+By+Cz+D=0, where [A,B,C] is the normal vector.

The Attempt at a Solution

I don't know. I can find the scalar equation of three separate points, but I am not sure here. Either I am not thinking about this the right way, or I am honestly lost.

 

[NewtonianAlch]

Well, you have two points given. From that you can get a vector.

Then you'll have two vectors since one is already given.

From there how would you get the normal vector?

 

[agenttiny200]

This is what I mean, not thinking. cross product, then I have normal vector, and I have my scalar equation.

Thanks for that.

 

[agenttiny200]

Just so that I don't have to start a new thread, I want to ask another question about scalar equations (Cartesian equations):
How do you find the scalar equation when given the vector equation of a line in 3-space?

I am given an equation like this:
[x, y, z] = [3, 1, 5] + s[-2, 3, -1] + t[2, 1, -2]

I am assuming I set one of the vectors as the origin, subtract it from the other vectors, and find the normal of the resulting vectors?

I am weak in my understanding of scalar equations and just want to double check to see if I am right.

 

[NewtonianAlch]

You are already given two vectors there.

You need to take the cross product of those two, which will give you the normal vector.