Find an equation of the plane?

Question

Find an equation of the plane that passes through the point P(-1, 2, 1) and contains the line of intersection of the planes x+y-z=2 and 2x-y+3z=1.

Answer 1

Concept: Three non-colinear points determine a plane.

Ideas of approach: Find the equation of the line first, and pick two points from the line plus the point P.

The equation of the line has a direction of <1, 1, -1> X <2, -1 ,3> = <2, -5, -3>

Pick one point from the line: <1, 1, 0>

So, the equation of the line is r = <1, 1, 0> + t<2, -5, -3>

Let t = 1 to get another point on the line <3, -4, -3>

With the three non-colinear points: <1, 1, 0>, <3, -4, -3> and <-1, 2, 1>, you can get the equation of the plane: x - 2y + 4z = -1.