Vectors

Question

Answer 1

The points are A = (-3, -3, -3), B = (-9, -6, 3) and C = (-6, -9, -9).

 

Answer 2

We can get two vectors in the plane by subtracting pairs of points in the plane:

We can get two vectors in the plane by subtracting pairs of points in the plane:

 

The equation of a plane is ax+by+cz = d, where

 is the normal vector to the plane.

 

We can plug a = -54, b = -54 and c = -27 to get -54x - 54y - 27z = d.

 

plug in the point (-9, -6, 3) to get -54(-9) -54(-6) -27(3) = d

 

d = -27 (2 * -9 + 2 * -6 + 3) = -27 (-18 -12 + 3) = -27 * 27

 

d = -2 7* 27

 

The equation of the plane is -54x - 54y - 27z = -27 * 27

 

2x + 2y - z = 27