find the general equation of the plane

Question

when you're given points (0,0,0) (0,2,-1) (-3,0,-4)?

Answer 1

Let the three points are P(0, 0, 0), Q(0, 2, -1) and R( -3, 0, -4)

Determine the direction vectors

Determine the normal vector

The plane is - 8x + 3y + 6z + d = 0

Substitute any point to find d.

Second point (0, 2, -1)

- 8(0) + 3(2) + 6(-1) + d = 0

0 + 6 - 6 + d = 0

d = 0

Substitute d  = 0 in plane equation.

- 8x + 3y + 6z + 0 = 0

Therfore, the equation of the plane is - 8x + 3y + 6z = 0.