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

Calculus 
MathMate,
I assume the plane needs to pass through the midpoint between the two points, and perpendicular to the line joining the two points.
First find the midpoint 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),12,44)=(4,1,8).
The equation for the plane is then:
4(xxm)(yym)8(zzm)=0
where M(xm,ym,zm) as calculated above.