1) Two vectors A and B are defined as A=aˆi and B=a(coswtˆi+sinwˆj), where a is a constant and w=π6rads−1 . If ∣A+B∣=√3∣A−B∣ at time t=τ for the first time, the value of τ in seconds, is A) 3.00 s B) 2.00 s C) 5.00 s D) 7.00 s Answer: Option BExplanation:A=aˆi and B=acosωˆi+asinωtˆj A+B=(a+acosωt)ˆi+asinωtˆj A−B=(a−acosωt)ˆi+asinωtˆj ∣A+B∣=√3∣A−B∣ √(a+acosωt)2+(asinωt)2=√3√(a−acosωt)2+(asinωt)2 ⇒ 2cosωt2=±√3×2sinωt2 tanωt2=±1√3 ωt2=nπ±π6 π12t=nπ±π6 t=(12n±2)s = 2 s