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# Solution for Write the Ratio in Which Yz-plane Divides the Segment Joining P (−2, 5, 9) and Q (3, −2, 4). - CBSE (Commerce) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### Question

Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).

#### Solution

$\text{ Let the YZ - plane divide the line segment joining points } P\left( - 2, 5, 9 \right) \text { and Q } \left( 3, - 2, 4 \right) \text{ in the ratio k: 1 } .$

$\text{ Using the section formula, the coordinates of the point of intersection are given by }$

$\left( \frac{k\left( 3 \right) - 2}{k + 1}, \frac{k\left( - 2 \right) + 5}{k + 1}, \frac{k\left( 4 \right) + 9}{k + 1} \right)$

$\text{ On the YZ - plane, the X - coordinate of any point is zero } .$

$\therefore \frac{k\left( 3 \right) - 2}{k + 1} = 0$

$\Rightarrow 3k - 2 = 0$

$\Rightarrow k = \frac{2}{3}$

$\text{ Thus, the YZ - plane divides the line segment formed by joining the given points in the ratio 2: 3 internally } .$

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#### Video TutorialsVIEW ALL [3]

Solution Write the Ratio in Which Yz-plane Divides the Segment Joining P (−2, 5, 9) and Q (3, −2, 4). Concept: Direction Cosines and Direction Ratios of a Line.
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