Question

Find the point on the line segment joining `P_1=(1, 4,-3)` and `P_2=(1, 5,-1)` that is `2/3` of the way from `P_1` to `P_2`.

Answer

`P=P_1+2/3(P_2-P_1)=(1,4,-3)+2/3(1-1,5-4,-1-(-3))=`

`=(1,4,-3)+2/3(0,1,2)=(1,4,-3)+(0,2/3,4/3)=`

`=(1+0,4+2/3,-3+4/3)=(1,14/3,-5/3)`.