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The Ratio in Which the Line Joining the Points (A, B, C) and (–A, –C, –B) is Divided by the Xy-plane is - Mathematics


The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is


  •  a : b

  •  b : c

  • c a

  • c : b

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 c : b

Let A\[\equiv\](a, b, c) and B\[\equiv\](\[-\]a,\[-\]c,\[-\]b)
Let the line joining A and B be divided by the xy-plane at point P in the ratio \[\lambda: 1\] 

Then, we have,

P\[\equiv \left( \frac{- a\lambda + a}{\lambda + 1}, \frac{- c\lambda + b}{\lambda + 1}, \frac{- b\lambda + c}{\lambda + 1} \right)\]

Since P lies on the xy-plane, the z-coordinate of P will be zero.

\[\therefore \frac{- b\lambda + c}{\lambda + 1} = 0\]
\[ \Rightarrow - b\lambda + c = 0\]
\[ \Rightarrow \lambda = \frac{c}{b}\]

Hence, the xz-plane divides AB in the ratio c : b 

  Is there an error in this question or solution?
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RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Q 2 | Page 22
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