Ex 10.2, 18 (MCQ) - Chapter 10 Class 12 Vector Algebra

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Ex 10.2, 18 - In triangle ABC which is not true AB + BC + CA = 0

Ex 10.2, 18 - Chapter 10 Class 12 Vector Algebra - Part 2
Ex 10.2, 18 - Chapter 10 Class 12 Vector Algebra - Part 3

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Ex 10.2, 18 In triangle ABC (Fig 10.18),which of the following is not true (A) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— + (𝐢𝐴) βƒ—= 0 βƒ— (B) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— – (𝐴𝐢) βƒ—= 0 βƒ— (C) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— – (𝐢𝐴) βƒ—= 0 βƒ— (D) (𝐴𝐡) βƒ— – (𝐢𝐡) βƒ— + (𝐢𝐴) βƒ—= 0 βƒ— In Ξ” ABC, (𝐴𝐢) βƒ— is the resultant of (𝐴𝐡) βƒ— & (𝐡𝐢) βƒ— (𝐴𝐢) βƒ— = (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— = (𝐴𝐢) βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (𝐴𝐢) βƒ— = 0 βƒ— Checking part (A) (𝑨𝑩) βƒ— + (𝑩π‘ͺ) βƒ— + (π‘ͺ𝑨) βƒ—= 𝟎 βƒ— From (1) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (𝐴𝐢) βƒ— = 0 βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (βˆ’(𝐢𝐴) βƒ—) = 0 βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— + (𝐢𝐴) βƒ— = 0 βƒ— Hence, (A) is true. Checking part (B) (𝑨𝑩) βƒ— + (𝑩π‘ͺ) βƒ— – (𝑨π‘ͺ) βƒ—= 𝟎 βƒ— From (1) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (𝐴𝐢) βƒ— = 0 βƒ— Hence, (B) is true. Checking part (C) (𝑨𝑩) βƒ— + (𝑩π‘ͺ) βƒ— – (π‘ͺ𝑨) βƒ—= 𝟎 βƒ— From (1) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (𝐴𝐢) βƒ— = 0 βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (βˆ’(𝐢𝐴) βƒ—) = 0 βƒ— (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— + (𝐢𝐴) βƒ— = 0 βƒ— Hence, (C) is not true. Checking part (D) (𝑨𝑩) βƒ— – (π‘ͺ𝑩) βƒ— + (π‘ͺ𝑨) βƒ—= 𝟎 βƒ— From (1) (𝐴𝐡) βƒ— + (𝐡𝐢) βƒ— βˆ’ (𝐴𝐢) βƒ— = 0 βƒ— (AB) βƒ— βˆ’ (CB) βƒ— + (CA) βƒ— = 0 βƒ— Hence, (D) is true. Thus, (C) is the correct option

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo