If a , b and c are three vectors such that | a |=| b |=2, a b =2 and a + b + c =0 , then | c | is equal to

Step-by-step solution

Given, |a |= |b|= 2, a ×b = 2 and a + b + c = 0, then|c|= ? a + b + c = 0 … (i) aligned & | a + b + c |^2=0 & | a |^2+| b |^2+| c |^2+2( a b + b c + c a )=0 & 2^2+2^2+| c |^2+2[2+ c ( a + b )]=0 & 4+4+| c |^2+2[2+ c (- c )]=0 & from Eq. (i), a + b =- c & 8+| c |^2+4-2| c |^2=0 & | c |^2=12 | c |=2 3 & aligned