Misc 5 - A point R with x-coordinate 4 lies on line segment - Miscellaneous

  1. Chapter 12 Class 11 Introduction to Three Dimensional Geometry
  2. Serial order wise
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Misc 5 A point R with x-coordinate 4 lies on the line segment joining the points P (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by ﷐﷐8k+2﷮k+1﷯,﷐−3﷮k+1﷯,﷐10k+4﷮k+1﷯﷯] Given that Point R lie on the line segment PQ. and x – Coordinate of R is 4 Let Point R be (4, b, c) Let R divide line segment PR in the ratio k : 1 We know that Coordinate of Point that divide line segment joining (x1 y1 z1) & (x2 y2 z2) in the ratio m : n is ﷐﷐﷐𝑚𝑥﷮2﷯+ ﷐𝑛𝑥﷮1﷯﷮𝑚+𝑛﷯,﷐﷐𝑚𝑦﷮2﷯+ ﷐𝑛𝑦﷮1﷯﷮𝑚+𝑛﷯,﷐﷐𝑚𝑧﷮2﷯+ ﷐𝑛𝑧﷮1﷯﷮𝑚+𝑛﷯﷯ Here, m = k , n = 1 x1 = 2 , y1 = – 3 , x2 = 8 , y2 = 0 Putting values R = ﷐﷐𝑘﷐8﷯+1(2)﷮𝑘+1﷯,﷐𝑘﷐0﷯+1(−3)﷮𝑘+1﷯,﷐𝑘﷐10﷯+1(4)﷮𝑘+1﷯﷯ (4, b, c) = ﷐﷐8𝑘+2﷮𝑘+1﷯,﷐0−3﷮𝑘+1﷯,﷐10𝑘+4﷮𝑘+1﷯﷯ (4, b, c) = ﷐﷐8𝑘+2﷮𝑘+1﷯,﷐−3﷮𝑘+1﷯,﷐10𝑘+4﷮𝑘+1﷯﷯

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