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# Xoz-plane Divides the Join of (2, 3, 1) and (6, 7, 1) in the Ratio - Mathematics

MCQ

XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

#### Options

• 3 : 7

•  2 : 7

• –3 : 7

•  –2 : 7

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#### Solution

−3:7

Let A$\equiv$(2, 3, 1) and B$\equiv$Let the line joining A and B be divided by the xz-plane at point P in the ratio$\lambda: 1$

Then, we have,

P$\equiv \left( \frac{6\lambda + 2}{\lambda + 1}, \frac{7\lambda + 3}{\lambda + 1}, \frac{\lambda + 1}{\lambda + 1} \right)$

Since P lies on the xz-plane, the y-coordinate of P will be zero.

$\therefore \frac{7\lambda + 3}{\lambda + 1} = 0$
$\Rightarrow 7\lambda + 3 = 0$
$\Rightarrow \lambda = \frac{- 3}{7}$

Hence, the xz-plane divides AB in the ratio $-$3 : 7

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Q 8 | Page 23
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