First slide
Introduction to 3-D Geometry
Question

 If the point x1+tx2x1,y1+ty2y1,z1+z2z1 devides the line segment joining x1,y1,z1)

 and x2,y2,z2 internally then 

Moderate
Solution

x1+tx2x1,y1+ty2y1,z1+z2z1=tx2+1-tx1,ty2+1-ty,tz2+1-tz1                                                                =tx2+1-tx1t+1-t,ty2+1-ty1t+1-t,tz2+1-tz1t+1-t the ratio of division is t:1-t Since the division is internal, t1-t>0 tt-1<0 0<t<1

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