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Q.
Find the coordinates of the point which is three fifth of the way from $(3,4,5)$ to $(-2, -1,0)$.
Introduction to Three Dimensional Geometry
Solution:
Let $A = (3,4 ,5)$, $B = (-2 ,-1,0)$ and $P (x, y, z)$ be the required point. As $P$ is three-fifth of the way from $A$ to $B$. So, $P$ divides $[AB]$ in the ratio $3 : 2$.
$\therefore P \equiv \left(\frac{3\times\left(-2\right)+2\times 3}{3+2}, \frac{3\times \left(-1\right)+2\times 4}{3+2}, \frac{3\times 0+2\times 5}{3+2}\right)$,
$\Rightarrow P = \left(0,1, 2\right)$.