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  4. 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

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Q. 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

EAMCETEAMCET 2014

Solution:

Using internally ratio formula, $(-2,3,5)$
$=\left(\frac{1 \times x+3 \times 1}{1+3}, \frac{1 \times y+3 \times 3}{1+3}, \frac{1 \times z+3 \times 4}{1+3}\right)$
$\Rightarrow (2,3,5)=\left(\frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4}\right)$
$\Rightarrow x+3=-8, y+9=12, z=12=20$
$\Rightarrow x=-11, y=+3, z=8$
$\therefore $ Required point $=B(-11,3,8)$