(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

vector cross product

ax + by + cz = 0

3. 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?

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# Finding cartesian equation of plane from 3 points

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