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
- At = π 2 ω
- Bt = π ω
- Ct = 0
- 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