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)

$-1$

For the line segment $QR$, let $P$ point divide in ratio $\lambda :1$, the coordinates aof $P$ are :

$X$ coordinate$=\frac{\lambda x_2+x_1}{\lambda +1}$

$y=Y$ coordinate $=\frac{\lambda y_2+y_1}{\lambda +1}$

According to question,

$(x_1,y_1,z_1)=(2,2,1)$ and $(x_2,y_2,z_2)=(5,1,-2)$

Since $X=4$

$4=\frac{5\lambda +2}{\lambda +1}$

$4\lambda +4=5\lambda =2$

$\lambda =2$

$Z$ coordinate of $P$ =$\frac{\lambda z_2+z_1}{\lambda +1}$

$=\frac{2\times (-2)+1}{2+1}$

$\frac{-4+1}{3}=-1$

Option $\text{B}$ is correct