Question

Find an equation of the plane that passes through the point (1,-1,1) and contains the line with symmetric equations x=2y=3z

Answer 1

So the equation for the line is \[r=(0,0,0,)+t(1,1/2,1/3)\] and then there is the point 1,-1,1 and I need the plane that contains both of them

Answer 2

So to me, the parametric equation of the line is what you already mentioned in your post, and now we need to find the plane that includes both of them, the line goes through the origin, therefore the plane also has to go through the origin. This means we can compute the normal vector the plane with the vector product of the point (as a origin vector) and the vector given by the line.

Answer 3

Do you mean (1,1/2,1/3)x(1,-1,1)