A point $P$ lies on the line joining $A(1,2,3)$ and $B(2,10,1)$. If $z$-coordinate of P is 7 , what is the sum of other two coordinates?

• Correct answer
  A

  -15
• B

  -13
• C

  -11
• D

  -9

Solution

Let $\mathrm{AP}: \mathrm{BP}=\mathrm{k}: 1$ $7=\frac{\mathrm{k}+3}{\mathrm{k}+1} \Rightarrow \mathrm{k}=\frac{-2}{3}$ So ratio is $2: 3$ externally. $\begin{aligned} & \text { Now, } x=\frac{2 \times 2-3 \times 1}{2-3}=-1 \\ & y=\frac{2 \times 10-3 \times 2}{2-3}=-14 \\ & \Rightarrow x+y=-15 \end{aligned}$

Hence, the correct answer is option: 'A'.