Equation of a plane given point P and a line

[Jm4872]

Homework Statement

Find the equation of the plane containing P(2,1,-1) and the line with equation
x=2+t
y=4
z=-1+t

Homework Equations

Cross product

The Attempt at a Solution

I understand that I need to find t and then solve for two points on the line, then find the cross product of both points with point P. I'm just confused as to how to determine the value for t, is it just arbitrary or is there a certain method that needs to be used in order to solve for the two values that I need?

Thanks!

 

[Dick]

You can do it that way by choosing any two values of t to get the points. Different choices of t will give you different cross products, but they will all point in the same direction. You could also just use the direction vector for the line.

 

[Jm4872]

Thanks !
I ended up using the direction vector and the point used to create the equation of the line and then cross product to get my answer!