Posted by **j** on Friday, May 25, 2012 at 12:12pm.

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

- Calculus -
**MathMate**, Friday, May 25, 2012 at 1:40pm
I assume the plane needs to pass through the mid-point between the two points, and perpendicular to the line joining the two points.

First find the mid-point by

M((x1+x2)/2,(y1+y2)/2,(z1+z2)/2)

The normal vector for the plane is just the vector AB, or N(3-(-1),1-2,-4-4)=(4,-1,-8).

The equation for the plane is then:

4(x-xm)-(y-ym)-8(z-zm)=0

where M(xm,ym,zm) as calculated above.

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