# Example 7 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 7 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 (i) internally, Let the 2 given points be A (1, 2, 3) & B (3, 4, – 5) Let P (x, y, z,) be points that divides line in ratio 2:3 internally We know that Co-ordinate of point P (x, y, z) that divides the line segment joining A (x1, y1, z1) & B (x2, y2, z2) internally in the ratio m : n is P (x, y, z,) = 𝑚 𝑥2+ 𝑛 𝑥1𝑚+𝑛,𝑚 𝑦2+ 𝑛 𝑦1𝑚+𝑛,𝑚 𝑧2+ 𝑛 𝑧1𝑚+𝑛 Here, x1 = 1, y1 = – 2, z1 = 3 x2 = 3, y2 = 4, z2 = – 5 & m = 2, n = 3 Putting values Co-ordinate of point P of (x, y, z) = 2(3) + 312+3,24 + 3−22 + 3,2−5 + 332 + 3 = 6 + 35,8 − 65,−10 + 95 = 95,25,−15 Thus, the required co-ordinate is 95,25,−15 Example 7 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 (ii) externally, Let the 2 given points be A (1, 2, 3) & B (3, 4, – 5) Let P (x, y, z,) be points that divides line in ratio 2:3 internally We know that Co-ordinate of point P (x, y, z) that divides the line segment joining A (x1, y1, z1) & B (x2, y2, z2) externally in the ratio m : n is P (x, y, z,) = 𝑚 𝑥2− 𝑛 𝑥1𝑚−𝑛,𝑚 𝑦2− 𝑛 𝑦1𝑚−𝑛,𝑚 𝑧2− 𝑛 𝑧1𝑚−𝑛 Here, x1 = 1, y1 = – 2, z1 = 3 x2 = 3, y2 = 4, z2 = – 5 & m = 2, n = 3 Putting values Co-ordinate of point P is (x, y, z) = 2(3) − 312−3,24 − 3−22 − 3,2−5 − 332 − 3 = 6 − 3(−1),8 + 6(−1),−10 − 9(−1) = 3(−1),14(−1), −19(−1) = ( – 3 , – 14 , 19) Thus, the required co-ordinate is (– 3 , – 14 , 19)

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