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Chapter 12 Class 11 - Intro to Three Dimensional Geometry
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Misc 3 - If origin is centroid of PQR with P (2a, 2, 6) - Miscellaneou

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

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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 ((𝑥_1 + 𝑦_1 + 𝑧_1)/3,(𝑥_2 + 𝑦_2 + 𝑧_2)/3,(𝑥_3 + 𝑦_3 + 𝑧_3)/3) 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) + 8)/3,(2 + 3𝑏 + 14)/3,(6 + (−10) + 2𝑐)/3) (0, 0, 0) = ((2𝑎 − 4 + 8)/3,(2 + 3𝑏 + 14)/3,(6 − 10 + 2𝑐)/3) (0, 0, 0) = ((2𝑎 + 4)/3,(3𝑏 + 16)/3,(2𝑐 − 4)/3) x – coordinate 0 = (2𝑎 + 4)/3 3(0) = 2a + 4 0 = 2a + 4 2a + 4 = 0 2a = – 4 a = (−4)/2 a = –2 y – coordinate 0 = (3𝑏 + 16)/3 0(3) = 3b + 16 0 = 3b + 16 3b +16 = 0 3b = – 16 b = (−16)/3 z – coordinate 0 = (2𝑐 − 4)/3 3(0) = 2c – 4 0 = 2c – 4 2c – 4 = 0 2c = 4 c = 4/2 c = 2 Thus, a = – 2 , b = (−𝟏𝟔)/𝟑 & c = 2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.