If the line joining A(1,3,4) and B is divided by the point ( –2,3,5) in the ratio 1:3 then B is ....

The given points are $A\left(1,1,4\right)$ and $B\left(a,b,c\right)$

The point $C\left(-2,3,5\right)$ dividws the line segment $AB$ in the ratio $1+2:-2-a=1:3$

It im[lies that $\frac{3}{-2-a}=\frac{1}{3}\Rightarrow -2-a=9\Rightarrow a=-11$

And the ratio also equal to $2-3:3-b=1:3$

It implies that $$\begin{gathered} \frac{2}{b-3}=\frac{1}{3} \\ b-3=6 \\ b=9 \end{gathered}$$