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NEET2015PhysicsMathematics in PhysicsActual

If vectors A → = cos ⁡ ω t  i ^ + s i n ω t   j ^ and B → = c o s ω t 2  i ^ + sin ⁡ ω t 2  j ^ are functions of time, then the value of t at which they are orthogonal to each other is:

Options

  1. At = π 2 ω
  2. Bt = π ω
  3. Ct = 0
  4. Dt = π 4 ω

Correct answer

B. t = π ω

Step-by-step solution

A → = cos   w t i ^ + sin w t j ^ B → = c o s w t 2 i ^ + s i n w t 2 j ^ For these vectors to be orthogonal, A → · B → = 0 A → · B → = 0 = cos   w t . cos w t 2 + sin   w t . sin   w t 2 = cos w t - w t 2 = cos w t 2 = 0 So, as we know, ( (90)=0 ). So, w t 2 = π 2 ⇒   t = π w

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