Misc 3 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry (Important Question)
Last updated at May 6, 2024 by Teachoo
Chapter 12 Class 11 Introduction to Three Dimensional Geometry
Chapter 12 Class 11 Introduction to Three Dimensional Geometry
Last updated at May 6, 2024 by Teachoo
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