Question

If x co-ordinates of a point P of line joining the points Q(2, 2, 1) and R(5, 2, -2) is 4, then the z-coordinates of P is
[RPET 2000]

• A. -2
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is B

-1

Suppose P divides QR in the ratio $\lambda :1.$
Then co-ordinates of P are $(\frac{5\lambda +2}{\lambda +1},\frac{\lambda +2}{\lambda +1},\frac{-2\lambda +1}{\lambda +1}.)$
It is given that the x-coordinate of P is 4. i.e., $\frac{5\lambda +2}{\lambda +1}=4\Rightarrow \lambda =2,$
So, z-coordinate of P is $\frac{-2\lambda +1}{\lambda +1}=\frac{-4+1}{2+1}=-1.$