Question

$A=(1,-1,2)$ and $B=$ $(2,3,7)$ are two points. lf $P,O$ divide $AB$ in the ratios $2:3,-2:3$ respectively then $P_x+Q_y=$

• A. $\frac{-38}{5}$
• B. $\frac{38}{5}$
• C. $\frac{-2}{5}$
• D. $\frac{-47}{6}$

Answer 1

The correct option is A $\frac{-38}{5}$

P divides line joining $A(1,-1,2)$ and $B(2,3,7)$ in the ratio $2:3$

$\therefore P_x=\frac{2\times 2+3\times 1}{2+3}=\frac{7}{5}$

Similarly, Q divides line joining $A(1,-1,2)$ and $B(2,3,7)$ in the ratio $-2:3$

$\therefore Q_y=\frac{-2\times 3+3\times -1}{-2+3}=-9$

$\Rightarrow P_x+Q_y=-9+\frac{7}{5}=\frac{-38}{5}$