Two vectors and are defined as and

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a\hat{i}

and

\vec{B} = a(\cos \omega t \hat{i} + \sin \omega t \hat{j})

, where

a

is a constant and

\omega = \pi/6

rad

s^{-1}

. If

|\vec{A} + \vec{B}| = \sqrt{3}|\vec{A} - \vec{B}|

at time

t = \tau

for the first time, the value of

\tau

, in seconds, is _____. [Adv. 2018]