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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

Transcript

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. (Using prop : (𝐴𝐢) βƒ— = βˆ’(𝐢𝐴) βƒ—) 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
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.