Example 20 - Chapter 10 Class 12 Vector Algebra
Last updated at May 29, 2018 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.
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 Important
Example 15
Example 16 Important
Example 17
Example 18
Example 19
Example 20 You are here
Example 21 Important
Example 22
Example 23 Important
Example 24 Important
Example 25 Important
Example 26
Example 27
Example 28 Important
Example 29 Important
Example 30 Important
Example 26 (Supplementary NCERT)
Example 27 (Supplementary NCERT)
Example 28 (Supplementary NCERT)
Example 29 (Supplementary NCERT)
Example 30 (Supplementary NCERT)
Example 31 (Supplementary NCERT)
About the Author
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.