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INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSINTRODUCTION TO THREE DIMENSIONAL GEOMETRY2 Marks
Question
Given that P(3,2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.
✓

Answer

Let Q(5, 4, -6) divides the line segment joining points P(3, 2, -4) and R(9, 8, -10) in the ratio k : 1 internally.
$\therefore$ Then coordinates of Q are $\left( {\frac{{9k + 3}}{{k + 1}},\;\frac{{8k + 2}}{{k + 1}},\;\frac{{ - 10k - 4}}{{k + 1}}} \right)$
But it is given that coordinates of Q is (5, 4, -6)
$\therefore \frac{{9k + 3}}{{k + 1}}=5 \ \Rightarrow$ 9k + 3 = 5

$\Rightarrow 9k+3=5(k+1)\\ \Rightarrow 9k+3=5k+5 \\ \Rightarrow 4k=2\\ \Rightarrow k=\frac{1}{2} $
Thus Q divides the line segment joining points P and R in the ratio $\frac{1}{2}:1$ i.e. 1 : 2 internally.

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