Question 1 (i) - Section - Defination - Chapter 11 Class 11 - Intro to Three Dimensional Geometry

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Question 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))