Question

Find co-ordinate of the point which divide the line segment joining the points $A(4,-2,5)$ and $(-2,3,7)$ externally in the ratio $8:5$.

Answer 1

Let $A$ be $(4,-2,5)$ and $B$ be $(-2,3,7)$

Let $P(x,y,z)$ be points that divide the line in ratio $8:5$ externally.

we know that

Co-ordinate of point $P(x,y,z)$ that divides the line segment joining A$(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$externally in the ratio

$m:n$ is:

$p(x,y,z)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$

$=(\frac{8.(-2)+5\left(4\right)}{8+5},\frac{8\left(3\right)+5(-2)}{8+5},\frac{8\left(7\right)+5\left(5\right)}{8+5})$

$=(\frac{-16+20}{13},\frac{24-10}{13},\frac{56+25}{13})$

$=(\frac{4}{13},\frac{14}{13},\frac{81}{13})$