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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

A point P lies on the line joining A(1,2,3) and B(2,10,1) . If z...

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

Options

  1. A-15
  2. B-13
  3. C-11
  4. D-9

Correct answer

A. -15

Step-by-step solution

Let AP:\mathrm{AP}:\mathrm{BP}=\mathrm{k}:17=k+3k+1⇒k=−23: 17=\frac{\mathrm{k}+3}{\mathrm{k}+1} \Rightarrow \mathrm{k}=\frac{-2}{3} So ratio is 2:32: 3 externally.  Now, x=2×2−3×12−3=−1y=2×10−3×22−3=−14⇒x+y=−15\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}
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