Example 20 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 24, 2019 by Teachoo
Transcript
Example 20 For any two vectors and , we always have | + | | | + | | (triangle inequality). To Prove: | + | | | + | | We first prove trivially, Therefore, the inequality | + | | | + | | is satisfied trivially. Now, let us assume 0 & 0 | + |2 = ( + ) . ( + ) = . + . + . + . = . + . + . + . = . + 2 . + . = | |2 + 2 . + | |2 = | |2 + 2| || | cos + | |2 | + |2 = | |2 + 2| || | cos + | |2 We know that cos 1 Multiplying 2| || | on both sides 2| || | cos 2| || | Adding | |2 + | |2 on both sides, | |2 + | |2 + 2| || | cos | |2 + | |2 + 2 | | | | | + |2 (| | + | |) 2 Taking square root both sides | + | (| | + | |) Hence proved.
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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.