How Do You Find the Equation of a Plane Through a Point and Containing a Line?

[kid2]

how do i work this?

find an equation for the plane that passes through the point (1,3,1) and contains the line x=t,y=t,z=-2+t

would the line equation be -2i+t(i+j+k)? and then would that mean that the direction or normal vector for the plane be i+j+k? and then what do you do? i have the answer and i can't get it...

 

[stunner5000pt]

to find the equation of a plane you need to have TWO distinct directional vectors and one point the plane passes through

you have been told that it contains the line - what is the directional vector of that line
you need one more directional vector - a vector between the line and the point will give you this. Pick a point on the given line and find the vector between this point and the given point.
the equation of the plane will look like this

$$P = (x,y,z) + sd_{1} + td_{2}$$
where s and t are scalar mutliples, d1 and d2 the directional vectors and x y z is the point

p.s. there are many possible answers