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Introduction to Three Dimensional Geometry — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSIntroduction to Three Dimensional Geometry1 Mark
Question
Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) in the ratio 2 : 3 internally.
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Answer

Let P (x, y, z) be the point which divides the line segment joining A(1, – 2, 3) and B (3, 4, –5) internally in the ratio 2 : 3. Therefore
$x=\frac{2(3)+3(1)}{2+3}=\frac{9}{5}, y=\frac{2(4)+3(-2)}{2+3}=\frac{2}{5}, z=\frac{2(-5)+3(3)}{2+3}=\frac{-1}{5}$ [using section formula]
Thus, the required point is $\left(\frac{9}{5}, \frac{2}{5}, \frac{-1}{5}\right)$ 

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