Ex 12.3, 3 - Find ratio in which YZ-plane divides line - Ex 12.3

  1. Chapter 12 Class 11 Introduction to Three Dimensional Geometry
  2. Serial order wise
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Ex 12.3, 3 Find the ratio in which the YZ-plane divides the line segment formed by joining the points ( 2, 4, 7) and (3, 5, 8). Let AB be the line segment joining points A ( 2, 4, 7) & B (3, 5, 8) Let YZ Plane divide line AB at P (x, y, z) in the ratio k : 1 Co-ordinate of P that divide line segment joining point A (x1, y1, z1) & B((x2, y2, z2) in the ratio m : n is = 2+ 1 + , 2+ 1 2+ , 2+ 1 + Here, m = k , n = 1 x1 = 2, y1 = 4, z1 = 7 x2 = 3, y2 = 5, z2 = 8 Co- ordinate of P P (x, y , z) = 3 + 1 2 + 1 , 5 + 1 4 + 1 , 8 + 1 7 + 1 (x, y , z) = 3 2 k + 1 , 5 + 4 k + 1 , 8 + 7 k + 1 Since Point p (x, y, z) lie on the YZ plane its x coordinate will be zero P(0, y , z) = 3 2 k + 1 , 5 + 4 k + 1 , 8 + 7 k + 1 Comparing x Co- ordinate 0 = 3 2 + 1 (k + 1) (0) = 3k 2 0 = 3k 2 3k 2 = 0 3k = 2 k = 2 3 1 = 2 3 k : 1 = 2 : 3 Thus, YZ plane divides AB in the ratio 2 : 3

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