Two vectors A → a n d B → are defined as A → = a i ^ a n d B → = a cos ⁡ ω t i ^ + sin ⁡ ω t j ^ , where a is a constant and ω = π 6 r a d s - 1 . If A → + B → = 3 A → - B → at time t = τ for the firs

Question

Two vectors A → a n d B → are defined as A → = a i ^ a n d B → = a cos ⁡ ω t i ^ + sin ⁡ ω t j ^ , where a is a constant and ω = π 6 r a d s - 1 . If A → + B → = 3 A → - B → at time t = τ for the first time, the value of τ in seconds, is_______

TestHub · Accepted Answer

A → + B → = 2 a cos ⁡ ω t 2 A → - B → = 2 a sin ⁡ ω t 2 So 2 a cos ⁡ ω t 2 = 3 2 a sin ⁡ ω t 2 tan ⁡ ω t 2 = 1 3 ω t 2 = π 6 ⇒ ω t = π 3 π 6 t = π 3 t = 2.00 s e c

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