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Find the equation of a plane that contains the points (1, -2, 4), (4, 1, 7), and (-1, 5, 1).
Solution:
The first thing that we have to do is to write the equation of a plane that contains the first point as follows
Next, substitute the values of x, y, and z from the other two points to the above equation, we have
for (4, 1, 7), then the above equation becomes
for (-1, 5, 1), then the above equation becomes
If you add the two equations above, then we can solve for the value of A in terms of B as follows
Substitute the value of A to either of the two equations to solve for the value of C in terms of B as follows
Therefore, the equation of a plane is
Divide both sides of the equation by B and then simplify, we have
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