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AP EAMCET202119 Aug 2021Evening ShiftMathematicsVector AlgebraActual

Let x , y are real numbers. If a → = ( sin x ) i ^ + ( sin y ) j ^ and b → = ( cos x ) i ^ + ( cos y ) j ^ , then | a → × b → | is

Options

  1. A0
  2. BGreater than one
  3. CLess than or equal to 1
  4. DLess than 1

Correct answer

C. Less than or equal to 1

Step-by-step solution

Given, a → = ( sin x ) i ^ + ( sin y ) j ^ and b → = ( cos x ) i ^ + ( cos y ) j ^ Then, a → × b → = sin x cos y - cos x sin y k ^ = sin x - y k ^ Now, a → × b → = sin 2 x - y = sin x - y We know that value of sine lies between - 1 ,   1 ⇒ a → × b → ≤ 1

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