INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSINTRODUCTION TO THREE DIMENSIONAL GEOMETRY2 Marks
Question
Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, - 5, 8).
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Answer
Let the line joining the points A(-2, 4, 7) and B(3, -5, 8) be divided by the yz plane at a point C in the ration k : 1. Then coordinates of C are $\left( {\frac{{3k - 2}}{{k + 1}},\;\frac{{ - 5k + 4}}{{k + 1}},\;\frac{{8k + 7}}{{k + 1}}} \right)$ Since the point C lies on yz-plane so x = 0 $\therefore \frac{{3k - 2}}{{k + 1}} = 0 \Rightarrow 3k - 2 = 0 \Rightarrow k = \frac{2}{3}$ Thus the required ratio is $\frac{2}{3}:1$ i.e. 2 : 3.
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