Two vectors a and b are at an angle of 60^ with each other. Their resultant makes an angle of 45^ with a . If | b |=2 units, then | a | is

Step-by-step solution

Angle between the vectors is, =60^ . Angle between resultant and a is, =45^ . The above is shown in the below figure, From parallelogram law, & is related as, ( )= | b | ( ) | a |+| b | ( ) . Substituting all the corresponding given values in above relation, we have, aligned & (45^ )= 2 (60^ ) | a |+2 (60^ ) = 3 a+1 ,( | a |=a) & 1= 3 a+1 & a+1= 3 & a= 3 -1 . aligned