Question

The coodinates of the point which divides the line joining the points $(2,3,4)$ and $(3,-4,7)$ in the ratio $2:4$ externally is:

• A. $(10,1,1)$
• B. $(1,10,1)$
• C. $(10,-10,10)$
• D. $(1,1,10)$

Answer 1

The correct option is B $(1,10,1)$

Given: Let $A(2,3,4)$ and $B(3,-4,7)$ be the given points whihch are divided in the ration $2:4$ externally by point $P$
Using section formula for external division, we have the
$P(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n},\frac{m{z}_2-n{z}_1}{m-n})$
$P(\frac{2\times 3-4\times 2}{2-4},\frac{2\times (-4)-4\times 3}{2-4},\frac{2\times 7-4\times 4}{2-4})$
$P(\frac{-2}{-2},\frac{-20}{-2},\frac{-2}{-2})$
$\Rightarrow P(1,10,1)$