Finding the equation of the plan. Mediator of the segment of extreme A(1,-2,6) and B(3,0,0)
Answer:
$\displaystyle x+y-3z+8=0$
Hi
To find the answer you need to know two things :
- the mediating plane is orthogonal to the line segment $\displaystyle [AB]$ (this boils to saying that the plane is orthogonal to $\displaystyle \vec{AB}$)
- the midpoint of $\displaystyle [AB]$ is a point of the mediating plane.
Hello,
A mediator is perpendicular to the segment and passes throught the midpoint.
The coordinates of $\displaystyle \overrightarrow{AB}$ are $\displaystyle (2~,~2~,~-6)$
So the equation of the plan, which has $\displaystyle AB$ as orthogonal vector, will be :
$\displaystyle 2x+2y-6z+d=0$
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With d to determine. And for this, you will have to use the fact that it goes throught the midpoint of AB.
Coordinates of the midpoint of [AB] : $\displaystyle \left(\frac{3+1}{2}~,~\frac{-2+0}{2}~,~\frac{6+0}2\right)$, that is to say $\displaystyle (2~,~-1~,~3)$.
This point is on the plane, so substitute and get d.
After that, divide the equation by 2.