Question

For $A(1,2,3)$ and $B(5,6,7),$ find the points that divide $\overline{AB}$ from $A^{\prime }$ s side in the ratio $3:2$ and $-3:2.$

Answer 1

$x=\frac{15+2}{5},\frac{17}{5}$

$y=\frac{18+4}{5}=\frac{22}{5}$

$z=\frac{21+6}{5}=\frac{27}{5}$

$\therefore$ $P=(\frac{17}{5},\frac{22}{5},\frac{27}{5})$

$x=\frac{-15+2}{-1},\frac{-13}{-1}=13$

$y=\frac{-18+4}{-1}=\frac{-14}{-1}=14$

$z=\frac{-21+6}{-1}=15$

$\therefore$ $Q=(13,14,15)$