# Misc 3

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

Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

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.