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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2021 · Mathematics · Three Dimensional Geometry

The x y -plane divides the line segment joining the points (-1,3,4)...

The xyx y-plane divides the line segment joining the points (−1,3,4)(-1,3,4) and (2,−5,6)(2,-5,6)

Options

  1. Ainternally in the ratio 2:32: 3
  2. Binternally in the ratio 3:23: 2
  3. Cexternally in the ratio 2:32: 3
  4. Dexternally in the ratio 2:12: 1

Correct answer

C. externally in the ratio 2:32: 3

Step-by-step solution


P(x,y,z)=2k−1k+1,−5k+35+1,6k+4k+1∴P(x, y, z)=\frac{2 k-1}{k+1}, \frac{-5 k+3}{5+1}, \frac{6 k+4}{k+1}\therefore Point P(x,y,z)P(x, y, z) lies in xyx y-plane ∴z=0⇒6k+4k+1=0⇒k=−23\therefore z=0 \Rightarrow \frac{6 k+4}{k+1}=0 \Rightarrow k=-\frac{2}{3} Externally in the ratio 2:32: 3.
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