Posted by Stephanies on .
Find the equation of the plane for which each point is equidistant from P(2,1,1) and Q (4,7,9).
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linear algebra 
MathMate,
Distance between two points in space,
D = √((x1x0)²+(y1y0)²+(z1z0)²)
Equate the distance between any point in the required plane, (x,y,z) and P(xp,yp,zp) to that between (x,y,z) and Q(xq,yq,zq) to get:
(xxp)²+(yyp)²+(zzp)² = (xxq)²+(yyq)²+(zzq)²
2x(xpxq)+2y(ypyq)+2z(zpzq)  (xp²xq²+yp²yq²+zp²zq²) = 0
Check my algebra.