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Ncert Solutions Maths class 11th Maths Class 11th Introduction to Three Dimensional Geometry

14. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

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Payal Gupta | Contributor-Level 10

4 months ago

14. Let A(x₁, y₁, z₁) and B(x₂, y₂, z₂) trisect the line segment joining the points P(4, 2, –6) and Q(10, –16, 6).

Since A divides PQ internally in ratio 1 : 2. Then co-ordinates of A

= $(\frac{1 (10) + 2 (4)}{1 + 2}, \frac{1 (- 16) + 2 (2)}{1 + 2}, \frac{1 (6) + 2 (- 6)}{1 + 2})$

= $(\frac{10 + 8}{3}, \frac{- 16 + 4}{3}, \frac{6 - 12}{3})$

= $(\frac{18}{3}, \frac{- 12}{3}, \frac{- 6}{3})$

= (6, –4, –2)

Similarly B divides PQ internally in ratio 2 : 1. Then co-ordinates of B

= $(\frac{2 (10) + 1 (4)}{2 + 1}, \frac{2 (- 16) + 1 (2)}{2 + 1}, \frac{2 (6) + 1 (- 6)}{2 + 1})$

= $(\frac{20 + 4}{3} \cdot, \cdot \frac{- 32 + 2}{3} \cdot, \cdot \frac{12 - 6}{3})$

= $(\frac{24}{3}, \frac{- 30}{3}, \frac{6}{3})$

= (8, –10, 2)

Hence the points which trisects the line segment joining the points P(4, 2, –6) and Q(10, –16, 6) are (6, –4, –2) and (8, –1)

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14. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

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