Example 7 - Find coordinates of point which divides line

Example 7 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 2
Example 7 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 3

 

 

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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 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 = 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) + 3(1))/(2 + 3),(2(4) + 3(−2))/(2 + 3),(2(−5) + 3(3))/(2 + 3)) = ((6 + 3)/5,(8 − 6)/5,(−10 + 9)/5) = (9/5,2/5,(−1)/5) Thus, the required co-ordinate is (𝟗/𝟓,𝟐/𝟓,(−𝟏)/𝟓)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.