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) = 2 + 1 + , 2 + 1 + , 2 + 1 + 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) = 2 1 , 2 1 , 2 1 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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