Question

If R divides the line segment joining P(2, 3, 4) and Q (4, 5, 6) in the ratio -3 : 2, then the value of the parameter which represents R is

• A. $=(8,9,10)$
• B. $=(10,9,8)$
• C. $=(10,8,9)$
• D. $=(9,10,8)$

Answer 1

The correct option is A $=(8,9,10)$

Given,

$P(2,3,4),Q(4,5,6)$

Given Ratio

$=-\frac{3}{2}=\frac{m}{n}$

Let

$R$ be $(x_3,y_3,z_3)$

$R=(\frac{m{x}_2+nx}{m+n},\frac{m{y}_2+ny}{m+n}+\frac{m{z}_2+nz}{m+n})$

$=(\frac{-3\left(4\right)+2\left(2\right)}{-3+2},\frac{-3\left(5\right)+2\left(3\right)}{-3+2}+\frac{-3\left(6\right)+2\left(4\right)}{-3+2})$

$=(-\frac{8}{-1},-\frac{9}{-1},-\frac{10}{-1})$

$=(8,9,10)$