Find plane equidistant between two points

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September 14th 2010, 10:42 AM
seuzy13

Find plane equidistant between two points

Find an equation for the plane, each of whose points is equidistant from (-1, -4, -2) and (0, -2, 2).

I tried to work on this by setting two distance formulas equal to each other, but I didn't know how to handle the absolute value on both sides, and the d term kept canceling out.

Also, I'm really hoping the question is referring to points and not vectors using that notation.

$\frac{|-a-4b-2c+d|}{\sqrt{a^2 + b^2 +c^2}}=\frac{|-2b+2c+d|}{\sqrt{a^2 + b^2 +c^2}}$
September 14th 2010, 10:51 AM
Plato

It is just the plane containing the midpoint $\left(\frac{-1}{2},-3,0\right)$ with normal $<1,2,4>$
September 14th 2010, 11:01 AM
seuzy13

Quote:

Originally Posted by Plato

It is just the plane containing the midpoint $\left(\frac{-1}{2},-3,0\right)$ with normal $<1,2,4>$

Oh, I see. That makes sense. So hard to visualize in three dimensions!

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