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Homework Statement
Find a Cartesian equation of the plane P containing A (2, 0, −3) , B(1, −1, 6) and C(5, 5, 0) , and determine if point D(3, 2, 3) lies on P.
Homework Equations
vector cross product
ax + by + cz = 0
The Attempt at a Solution
Take the cross product of AB and AC to get normal vector.
AB = -i -j + 9k
AC = 31 + 5j + 3k
I used the determinant method at got:
AB X AC = -48i + 30j -2k
Now as A, B and C lie on P, take a point say A(2, 0, -3)
-48(x - 2) +30(y) -2(z + 3) = 0
rearranging that gives:
-48x + 30y -2z = -90
Then putting in the x, y and z values for D the equation holds.
The question I have is that the answer for the plane given is:
24x − 15y + z = 45
Is there a more common method to follow to get this equation rather than the one I got?