# Ex 12.3, 1 - Class 11

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

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 𝑥2+ 𝑛 𝑥1𝑚+𝑛,𝑚 𝑦2+ 𝑛 𝑦1𝑚+𝑛,𝑚 𝑧2+ 𝑛 𝑧1𝑚+𝑛 Here, x1 = – 2, y1 = 3, z1 = 5 x2 = 1, y2 = – 4, z2 = 6 & m = 2 , n = 3 Putting values (x, y, z) = 21+ 3−22+3,2 −4+ 332+ 3,26+ 352+ 3 = 2 − 65,− 8 + 95,12 + 15 5 = −4 5,15,27 5 Thus, the required coordinate of point P is −4 5,15,27 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 𝑥2− 𝑛 𝑥1𝑚−𝑛,𝑚 𝑦2− 𝑛 𝑦1𝑚−𝑛,𝑚 𝑧2− 𝑛 𝑧1𝑚−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) − 3−22 − 3,2 −4 − 332 − 3,26 − 352 − 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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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.