Question

If $x$ -coordinate of a point $P$ on the line joining the points $Q(2,2,1)$ and $R(5,1,-2)$ is 4, then the $z$ -coordinate of $P$ is

• A. $-2$
• B. $-1$
• C. 1
• D. 2

Answer 1

Answer: (B)

Let $P$ divide $Q(2,2,1)$ and $R(5,1,-2)$ in the ratio of $m: 1$.
$\therefore P\left(\frac{5 m+2}{m+1}, \frac{m+2}{m+1}, \frac{-2 m+1}{m+1}\right)$
But it is given $\frac{5 m+2}{m+1}=4$.
$\Rightarrow 5 m+2=4 m+4$
$\Rightarrow m=2$
$\therefore $ Coordinate of $z=\frac{-2 \times 2+1}{2+1}=\frac{-3}{3}=-1$