# Example, 10 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example, 10 Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, – 8) is divided by the YZ-plane. Let AB be the line segment joining points A (4, 8, 10) & (6, 10, – 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 = 𝑚𝑥2 + 𝑛𝑥1𝑚 + 𝑛, 𝑚𝑦2 + 𝑛𝑦1𝑚 + 𝑛,𝑚𝑧2 + 𝑛𝑧1𝑚 + 𝑛 Here, m = k , n = 1 x1 = 4, y1 = 8, z1 = 10 x2 = 6 , y2 = 10, z2 = – 8 Co- ordinate of P P (x, y , z) = 𝑘 6 + 1 4𝑘 + 1, 𝑘10 + 18𝑘 + 1, 𝑘−8 + 110𝑘 + 1 (x, y , z) = 6𝑘 + 4k + 1,10k + 8k + 1,−8𝑘 + 10k + 1 Since Point p (x, y, z) lie on the YZ plane its x – coordinate will be zero P (0, y , z) = 6𝑘 + 4k + 1,10k + 8k + 1,−8𝑘 + 10k + 1 Comparing x – Coordinate 0 = 6𝑘 + 4𝑘 + 1 (k + 1) (0) = 6k + 4 0 = 6k + 4 6k + 4 = 0 6k = – 4 k = −46 k = −23 𝑘1 = −23 k : 1 = – 2 : 3 Since value of k is negative Hence YZ Plane divide AB externally in the ratio 2 : 3

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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.