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# If the X-coordinate of a Point P on the Join of Q (2, 2, 1) and R (5, 1, −2) is 4, Then Its Z-coordinate is (A) 2 (B) 1 (C) −1 (D) −2 - CBSE (Arts) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### Question

If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is

• 2

• 1

• -1

• -2

#### Solution

- 1

$\text { Suppose the point P divides the line joining the point Q } \left( 2, 2, 1 \right) \text{ and } R \left( 5, 1, - 2 \right) \text{ in the ratio k: 1 } .$

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

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

$\text { It is given that the X - coordinate of P is 4 } .$

$\Rightarrow \frac{k\left( 5 \right) + 2}{k + 1} = 4$

$\Rightarrow 5k + 2 = 4\left( k + 1 \right)$

$\Rightarrow k = 2$

$\text{ Now } ,$

$Z - \text{ coordinate of P } = \frac{k\left( - 2 \right) + 1}{k + 1}$

$= \frac{2\left( - 2 \right) + 1}{2 + 1} \left [ \text{ Substituting k } = 2 \right]$

$= - 1$

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Solution If the X-coordinate of a Point P on the Join of Q (2, 2, 1) and R (5, 1, −2) is 4, Then Its Z-coordinate is (A) 2 (B) 1 (C) −1 (D) −2 Concept: Direction Cosines and Direction Ratios of a Line.
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