Example 15 - Show vectors a + b and a - b are perpendicular - Scalar product - Solving

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

Transcript

Example 15 If = 5 3 and = + 3 5 , then show that the vectors + and are perpendicular. Two vectors and are perpendicular if their scalar product is zero, i.e. . = 0 = 5 3 = + 3 5 ( + ) = (5 + 1) + ( 1 + 3) + ( 3 + ( 5)) = 6 + 2 + 8 ( ) = (5 1) + ( 1 3) + ( 3 ( 5)) = 4 4 + 2 Now, we have to show that ( + ) and ( ) are perpendicular to each other. So, we need to show ( + ) . ( ) = 0 Taking LHS ( + ) . ( ) = (6 + 2 8 ) . (4 4 + 2 ) = (6 4) + (2 4) + ( 8 2) = 24 + ( 8) + (-16) = 24 + ( 24) = 0 Since ( + ) . ( ) = 0 Hence, ( + ) is perpendicular to ( )

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