If a point $\mathrm{P}$ on the line segment joining the points $(3,5,-1)$ and $(6,3,-2)$ has its y -…
If a point $\mathrm{P}$ on the line segment joining the points $(3,5,-1)$ and $(6,3,-2)$ has
its y - coordinate 2, then its z - coordinate is
$\frac{-2}{5}$
$\frac{17}{3}$
$\frac{-5}{2}$
$\frac{3}{17}$
Solution
Equation of line passing through $(3,5,-1)$ and $(6,3,-2)$ is
$\frac{x-3}{3}=\frac{y-5}{-2}=\frac{z+1}{-1}=r(\text { say })$
Hence coordinates of any point lying on the line are $(3 r+3,-2 r+5,-r-1)$
We have $-2 r+5=2 \quad \Rightarrow \quad r=\frac{3}{2}$
$\therefore \quad z$ coordinate is $\quad-r-1=\frac{-3}{2}-1=\frac{-5}{2}$