Last updated at Dec. 8, 2016 by Teachoo

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Ex 10.2, 18 In triangle ABC (Fig 10.18),which of the following is not true (A) π΄π΅ο·― + π΅πΆο·― + πΆπ΄ο·―= 0ο·― (B) π΄π΅ο·― + π΅πΆο·― β π΄πΆο·―= 0ο·― (C) π΄π΅ο·― + π΅πΆο·― β πΆπ΄ο·―= 0ο·― (D) π΄π΅ο·― β πΆπ΅ο·― + πΆπ΄ο·―= 0ο·― In Ξ ABC, π΄πΆο·― is the resultant of π΄π΅ο·― & π΅πΆο·― π΄πΆο·― = π΄π΅ο·― + π΅πΆο·― π΄π΅ο·― + π΅πΆο·― = π΄πΆο·― π΄π΅ο·― + π΅πΆο·― β π΄πΆο·― = 0ο·― Checking part (A) π¨π©ο·― + π©πͺο·― + πͺπ¨ο·―= πο·― From (1) π΄π΅ο·― + π΅πΆο·― β π΄πΆο·― = 0ο·― π΄π΅ο·― + π΅πΆο·― β (β πΆπ΄ο·―) = 0ο·― π΄π΅ο·― + π΅πΆο·― + πΆπ΄ο·― = 0ο·― Hence, (A) is true. Checking part (B) π¨π©ο·― + π©πͺο·― β π¨πͺο·―= πο·― From (1) π΄π΅ο·― + π΅πΆο·― β π΄πΆο·― = 0ο·― Hence, (B) is true. Checking part (C) π¨π©ο·― + π©πͺο·― β πͺπ¨ο·―= πο·― From (1) π΄π΅ο·― + π΅πΆο·― β π΄πΆο·― = 0ο·― π΄π΅ο·― + π΅πΆο·― β (β πΆπ΄ο·―) = 0ο·― π΄π΅ο·― + π΅πΆο·― + πΆπ΄ο·― = 0ο·― Hence, (C) is not true. Checking part (D) π¨π©ο·― β πͺπ©ο·― + πͺπ¨ο·―= πο·― From (1) π΄π΅ο·― + π΅πΆο·― β π΄πΆο·― = 0ο·― ABο·― β CBο·― + CAο·― = 0ο·― 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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.