# Misc 3 - 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

Misc 3 If origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (–4, 3b, –10) and R (8, 14, 2c), then find the values of a, b and c. Given Δ PQR where P (2a, 2, 6) , Q (4, 3b, –10) , R (8, 14, 2c) Also, Origin O (0, 0, 0) is the centroid of Δ PQR We know that Co ordinate of centroid whose vertices are (x1 , y1 ,z1) ,(x2 ,y2 ,z2) (x3 ,y3 ,z3) is 𝑥1 + 𝑦1 + 𝑧13,𝑥2 + 𝑦2 + 𝑧23,𝑥3 + 𝑦3 + 𝑧33 Here, x1 = 2a , y1 = 2 , z1 = 6 x2 = – 4 , y2 = 3b , z2 = –10 x3 = 8 , y2 = 14 , z3 = 2c ∴ Coordinates of centroid O(0, 0, 0) (0, 0, 0) = 2𝑎 + −4 + 83,2 + 3𝑏 + 143,6 + −10 + 2𝑐3 (0, 0, 0) = 2𝑎 − 4 + 83,2 + 3𝑏 + 143,6 − 10 + 2𝑐3 (0, 0, 0) = 2𝑎 + 43,3𝑏 + 163,2𝑐 − 43 Thus a = – 2 , b = −163 & c= 2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.