Question

The coordinates of the point where the line joining $P(3,4,1)$ and $Q(5,1,6)$ crosses the xy-plane are:

• A. $\left(-\frac{13}{5},-\frac{23}{5},0\right)$
• B. $\left(\frac{13}{5},\frac{23}{5},0\right)$
• C. $\left(\frac{13}{5},-\frac{23}{5},0\right)$
• D. $\left(-\frac{13}{5},\frac{23}{5},0\right)$

Answer 1

Answer: (B)

$\left(\frac{13}{5},\frac{23}{5},0\right)$

$P(3,4,1)$

$Q(5,1,6)$

Equation of PQ

$\frac{x-3}{5-3}=\frac{y-4}{1-4}=\frac{z-1}{6-1}\frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5}Inxyplanez=0\therefore \frac{z-1}{5}=\frac{-1}{5}\frac{x-3}{2}=\frac{-1}{5}x=3-\frac{2}{5}=\frac{13}{5}\frac{y-4}{-3}=\frac{-1}{5}y=4+\frac{3}{5}=\frac{23}{5}\therefore Coordinatesare(\frac{13}{5},\frac{23}{5},0)$