First slide
Introduction to 3-D Geometry
Question

The mid points of the sides of a triangle are   (1,5,1),(0,4,2),(2,3,4) . The distance from origin to the farthest vertex from origin is 

Easy
Solution

Given the midpoints of the sides of the triangle are D(1,5,1),E(0,4,2),F(2,3,4)

If D,E,F are the sides of the triangle ABC then A=E+F-D=1,2,3 , B=D+F-E=3,4,5 and C=D+E-F=1,6,-7

The distance of the vertices from the origin is 

OA=1+4+9=14OB=9+16+25=50OC=1+36+49=86

The point C is farthest point from origin and at it is a distance 86

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