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Ex 10.2, 18 - In triangle ABC which is not true AB + BC + CA = 0 - Addition(resultant) of vectors

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Ex 10.2, 18 In triangle ABC (Fig 10.18),which of the following is not true (A) 𝐴𝐡﷯ + 𝐡𝐢﷯ + 𝐢𝐴﷯= 0ο·― (B) 𝐴𝐡﷯ + 𝐡𝐢﷯ – 𝐴𝐢﷯= 0ο·― (C) 𝐴𝐡﷯ + 𝐡𝐢﷯ – 𝐢𝐴﷯= 0ο·― (D) 𝐴𝐡﷯ – 𝐢𝐡﷯ + 𝐢𝐴﷯= 0ο·― In Ξ” ABC, 𝐴𝐢﷯ is the resultant of 𝐴𝐡﷯ & 𝐡𝐢﷯ 𝐴𝐢﷯ = 𝐴𝐡﷯ + 𝐡𝐢﷯ 𝐴𝐡﷯ + 𝐡𝐢﷯ = 𝐴𝐢﷯ 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ 𝐴𝐢﷯ = 0ο·― Checking part (A) 𝑨𝑩﷯ + 𝑩π‘ͺο·― + π‘ͺ𝑨﷯= 𝟎﷯ From (1) 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ 𝐴𝐢﷯ = 0ο·― 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ (βˆ’ 𝐢𝐴﷯) = 0ο·― 𝐴𝐡﷯ + 𝐡𝐢﷯ + 𝐢𝐴﷯ = 0ο·― Hence, (A) is true. Checking part (B) 𝑨𝑩﷯ + 𝑩π‘ͺο·― – 𝑨π‘ͺο·―= 𝟎﷯ From (1) 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ 𝐴𝐢﷯ = 0ο·― Hence, (B) is true. Checking part (C) 𝑨𝑩﷯ + 𝑩π‘ͺο·― – π‘ͺ𝑨﷯= 𝟎﷯ From (1) 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ 𝐴𝐢﷯ = 0ο·― 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ (βˆ’ 𝐢𝐴﷯) = 0ο·― 𝐴𝐡﷯ + 𝐡𝐢﷯ + 𝐢𝐴﷯ = 0ο·― Hence, (C) is not true. Checking part (D) 𝑨𝑩﷯ – π‘ͺ𝑩﷯ + π‘ͺ𝑨﷯= 𝟎﷯ From (1) 𝐴𝐡﷯ + 𝐡𝐢﷯ βˆ’ 𝐴𝐢﷯ = 0ο·― ABο·― βˆ’ 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 contact him here.
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