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:

Question

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:, t = π 2 ω, t = π ω, t = 0, t = π 4 ω

MARKS App · Accepted Answer

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, $\cos (90)=0$. So, w t 2 = π 2 ⇒ t = π w

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