Ex 12.3, 1 - Find coordinates of point which divides - Ex 12.3

  1. Chapter 12 Class 11 Introduction to Three Dimensional Geometry
  2. Serial order wise
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Ex 12.3, 1 Find the coordinates of the point which divides the line segment joining the points (–2, 3, 5) and (1, –4, 6) in the ratio (i) 2:3 internally. Let A be (–2, 3, 5) & B be (1, –4, 6) Let coordinate of point P be (x, y, z) that divides the line joining A & B in the ratio of 2 : 3 internally We know that Coordinate of P that divide the line segment joining A(x1, y1, z1) & B(x2, y2, z2) internally in the ratio m: n is P(x, y, z) = ﷐﷐﷐𝑚 𝑥﷮2﷯+﷐ 𝑛 𝑥﷮1﷯﷮𝑚+𝑛﷯,﷐﷐𝑚 𝑦﷮2﷯+﷐ 𝑛 𝑦﷮1﷯﷮𝑚+𝑛﷯,﷐﷐𝑚 𝑧﷮2﷯+﷐ 𝑛 𝑧﷮1﷯﷮𝑚+𝑛﷯﷯ Here, x1 = – 2, y1 = 3, z1 = 5 x2 = 1, y2 = – 4, z2 = 6 & m = 2 , n = 3 Putting values (x, y, z) = ﷐﷐2﷐1﷯+ 3﷐−2﷯﷮2+3﷯,﷐2 ﷐−4﷯+ 3﷐3﷯﷮2+ 3﷯,﷐2﷐6﷯+ 3﷐5﷯﷮2+ 3﷯﷯ = ﷐﷐2 − 6﷮5﷯,﷐− 8 + 9﷮5﷯,﷐12 + 15﷮ 5﷯﷯ = ﷐﷐−4﷮ 5﷯,﷐1﷮5﷯,﷐27﷮ 5﷯﷯ Thus, the required coordinate of point P is ﷐﷐−4﷮ 5﷯,﷐1﷮5﷯,﷐27﷮ 5﷯﷯ Ex12.3, 1 Find the coordinates of the point which divides the line segment joining the points (–2, 3, 5) and (1, –4, 6) in the ratio (ii) 2:3 externally. Let A be (–2, 3, 5) & B be (1, –4, 6) Let coordinate of point P be (x, y, z) that divides the line joining A & B in the ratio of 2 : 3 externally We know that Coordinate of P that divide the line segment joining A(x1, y1, z1) & B(x2, y2, z2) externally in the ratio m: n is P(x, y, z) = ﷐﷐﷐𝑚 𝑥﷮2﷯−﷐ 𝑛 𝑥﷮1﷯﷮𝑚−𝑛﷯,﷐﷐𝑚 𝑦﷮2﷯−﷐ 𝑛 𝑦﷮1﷯﷮𝑚−𝑛﷯,﷐﷐𝑚 𝑧﷮2﷯−﷐ 𝑛 𝑧﷮1﷯﷮𝑚−𝑛﷯﷯ Here, x1 = – 2, y1 = 3, z1 = 5 x2 = 1, y2 = – 4, z2 = 6 & m = 2 , n = 3 Putting values (x, y, z) = ﷐﷐2(1) − 3﷐−2﷯﷮2 − 3﷯,﷐2 ﷐−4﷯ − 3﷐3﷯﷮2 − 3﷯,﷐2﷐6﷯ − 3﷐5﷯﷮2 − 3﷯﷯ = ﷐﷐2 + 6﷮ −1﷯,﷐− 8 − 9﷮− 1﷯,﷐12 −15﷮ −1﷯﷯ = ﷐﷐8﷮ −1﷯,﷐− 17﷮− 1﷯,﷐− 3﷮ −1﷯﷯ = ( – 8, 17, 3) Thus, the required coordinate of point P is (–8, 17, 3)

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