MCQ

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

#### Options

*a*:*b**b*:*c**c*:*a**c*:*b*

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#### Solution

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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