Question

Find the coordinates of the point , which divides the line segment joining the points $A(2,-6,8)$ and $B(-1,3,-4)$, externally in the ratio $1:3$.

Answer 1

Let the required point be $P(x,y,z)$

Then,

$x=\frac{1(-1)-3\left(2\right)}{1-3}=\frac{7}{2}$

$y=\frac{1\left(3\right)-3(-6)}{1-3}=\frac{-21}{2}$

$z=\frac{1(-4)-3\left(8\right)}{1-3}=14$

therefore required point is $(\frac{7}{2},\frac{-21}{2},14)$