# Find plane equidistant between two points

• Sep 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.

$\displaystyle \frac{|-a-4b-2c+d|}{\sqrt{a^2 + b^2 +c^2}}=\frac{|-2b+2c+d|}{\sqrt{a^2 + b^2 +c^2}}$
• Sep 14th 2010, 10:51 AM
Plato
It is just the plane containing the midpoint $\displaystyle \left(\frac{-1}{2},-3,0\right)$ with normal $\displaystyle <1,2,4>$
• Sep 14th 2010, 11:01 AM
seuzy13
Quote:

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

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