Find an equation of the plane?

Question

The Plane through the points (3,-1,2), (8,2,4), and (-1,-2,-3).


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Also, find the plane through the point (6,3,2) and perpendicular to the vector < -2, 1, 5 >.

Answer 1

One problem per question please.

Find the plane through the point P(6,3,2) and perpendicular to the vector n = < -2, 1, 5 >.

With the normal vector n, to the plane and a point P on the plane you can simply write the equation of the plane.

-2(x - 6) + 1(y - 3) + 5(z - 2) = 0
-2x + 12 + y - 3 + 5z - 10 = 0
-2x + y + 5z - 1 = 0

Answer 2

don't be lazy do your own homework