Determining a Cartesian equation given a point and a line

[raymondlk]

Homework Statement

Given the point P(-2,0,6) and the line "x-4/3= y+2/-5=z-1/2" determine the cartesian equation of the plane.

Homework Equations

the lines vector equation is (4,-2,1)+T(3,-5,2)

The Attempt at a Solution

using A(x,y,z) i attempted to find a directional vector for P, PA=(x+2,y,z-6). I figured the dot product of PA nad the directional vector of the line would give me the cartesian equation but it doesn't satisfy the given answer.
help?

 

[raymondlk]

Nvm guys, i got it...you can find another directional vector using points P and the coordinate given in the lines equation. That will give you directional vector (6,-2,-5), with this you find the cross product of the two directional vectors giving you (-29,-27,-24).
Then take the original coordinate, and coordinate A(x,y,z), PA=x+2, y ,z-6). find the dot product of the cross product and PA, and itll give you the cartesian equation!