Let | a |=2,| b |=3 and the angle between a and b be 3 . If a parallelogram is constructed with adjacent sides 2 a +3 b and a - b , then its shorter diagonal is of length

Step-by-step solution

gathered | a |=2,| b |=3, = 3 a b =| a || b | =6 1 2 =3 gathered Diagonals are p + q and p - q where aligned & p =2 a +3 b and q = a - b & | p + q |^2=|3 a +2 b |^2=9| a |^2+4| b |^2+12 a . b & =9 4+4 9+12 3=108 & | p + q |=6 3 aligned