Example 30 - With reference to right handed system of mutually - Scalar product - Defination

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Slide81.JPG

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

Example 30 If with reference to the right handed system of mutually perpendicular unit vectors , and , = 3 , = 2 + 3 , then express in the form = 1 + 2, where 1 is parallel to and 2 is perpendicular to . = 3 = 3 + 0 = 2 + 3 = 2 + 1 3 To show: = 1 + 2 Given, 1 is parallel to & 2 is perpendicular to Let 1 = , being a scalar. 1 = (3 1 + 0 ) = 3 + 0 Now, 2 = 1 = 2 + 1 3 3 + 0 = 2 + 1 3 3 + + 0 = (2 3 ) + (1 + ) 3 Also, since 2 is perpendicular to So, 2 . = 0 (2 3 ) + (1 + ) 3 . (3 1 + 0 ) = 0 (2 3 ) 3 + (1 + ) 1 + ( 3) 0 = 0 6 9 1 = 0 5 10 = 0 10 = 5 = 5 10 = Putting value of in 1 and 2 , 1 = 3 + 0 = 3. 1 2 1 2 + 0 = 2 = (2 3 ) + (1 + ) 3 = 2 3. 1 2 + 1+ 1 2 3 = + 3

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