Calculus
posted by Tom .
Find the vector and scalar equations of the plane containing the line r=(3,5,1)+t(2,3,1) and the point (1,2,3)

We know one direction vector of the plane is (2,3,1)
We have to find another.
Use the two points (3,5,1) and (1,2,3)
the vector would be (2,3,2)
I will assume you know how to find the crossproduct between these two vectors.
I got (9,2,12)
So the plane has equation
9x + 2y + 12z = c
plug in (1,2,3)
9 + 4 + 36 = c = 49
scalar equation is
9x + 2y + 12z = 49
vector equation is
r = (3,5,1) + t(2,3,1) + s(2,3,2)