Find an equation of a plane containing the three points (-2,-5,0), (0,0,3), (0,1,5) in which the coefficient of x is 7

Question

Find an equation of a plane containing the three points

(-2,-5,0), (0,0,3), (0,1,5)

in which the coefficient of x is 7

____________ = 0

Answer 1

The general equation of a plane is of the form

ax + by + cz + d = 0

We are told that a = 7.

We are given three points, which we can plug in to get three equations for the three unknowns b, c, d:

-2×7 - 5×b + 0×c + d = 0

0×7 + 0×b + 3×c + d = 0

0×7 + 1×b + 5×c + d = 0

Solving them gives

b = -4

c = 2

d = -6

The equation of the plane is

7x - 4y + 2z - 6 = 0