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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

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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Q 2 | Page 22
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