A = (1, -1, 2) and B = (2, 3, 7) are two points. lf P, O divide A… - Vidyadip

MCQ

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 $P_x+Q_y=$

✓
$\frac{-38}{5}$
B
$\frac{38}{5}$
C
$\frac{-2}{5}$
D
$\frac{-47}{6}$

✓

Answer

Correct option: A.

$\frac{-38}{5}$

$\frac{-38}{5}$

Solution:
P divides line joining A (1, -1, 2) and B (2, 3, 7) in the ratio 2 : 3
$\therefore\text{P}_{\text{x}}=\frac{2\times2+3\times1}{2+3}=\frac{7}{5}$ Similarly, Q divides line joining A (1, -1, 2) and B (2, 3, 7) in the ratio -2 : 3
$\therefore\text{Q}_{\text{y}}=\frac{-2\times3+3\times-1}{-2+3}=-9$
$\Rightarrow\text{P}_{\text{x}}+\text{Q}_{\text{y}}=-9+\frac{7}{5}=\frac{-38}{5}$

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