Posted by **j** on Saturday, May 26, 2012 at 8:11am.

5. Determine an equation for the plane that is exactly between the points A(-1, 2, 4) and B(3, 1, -4).

- Calculus -
**Reiny**, Saturday, May 26, 2012 at 8:34am
vector AB must be the normal to the plane

vector AB = (4,-1,-8)

so the plane must have equation:

4x - y - 8z = c

but the midpoint of AB must lie on it, and that midpoint is (1, 3/2, 0)

sub it in ...

4 - 3/2 - 0 = c

c = 5/2

plane equation:

4x - y - 8z = 5/2 or in only integers

8x - 2y - 16z = 5

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