1)

Two vectors A and B are defined as A=aˆi  and   B=a(coswtˆi+sinwˆj), where a is a constant  and w=π6rads1 . If  A+B∣=3AB  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 B

Explanation:

A=aˆi  and  B=acosωˆi+asinωtˆj

  A+B=(a+acosωt)ˆi+asinωtˆj

  AB=(aacosωt)ˆi+asinωtˆj

    A+B∣=3AB

      (a+acosωt)2+(asinωt)2=3(aacosωt)2+(asinωt)2

        2cosωt2=±3×2sinωt2

  tanωt2=±13

   ωt2=nπ±π6

   π12t=nπ±π6

     t=(12n±2)s

         = 2 s