Question

Two equal vector have their resultant equal to either of them at what angle they inclinded each other

Answer 1

Let the vectors be A and B ,

as vectors A and B are equal => A = B

Let angle between the vectors be @

Resultant of two vectors

= sqRoot ( A^2 + B^2 + 2 × A × B × Cos@ )

= SqRoot ( A^2 + A^2 + 2 × A × A × Cos@ ) ( since A = B )

= SqRoot ( 2A^2 + 2 × A^2 × Cos@ )

= SqRoot { 2 × A^2 ( 1 + Cos @ ) }

= SqRoot { 2 × A^2 × 2 × Cos^2 ( @ /2 ) }

( since 1 + Cos@ = 2 Cos^2 ( @ /2 ) )

= SqRoot ( 4 × A^2 × Cos^2 (@/2) )

= 2 × A × Cos (@/2)

Thus Resultant = 2A × Cos(@/2)

It is given that Resultant of the two vector is equal to the either of the two vectors

=> Resultant = A or B

=> Resultant = A

=> 2A × Cos (@/2 ) = A

=> cos (@/2) = A / 2A

=> Cos (@/2) = 1/2

=> Cos (@/2) = Cos 60°

=> @/2 = 60 °

=> @ = 120°

So the two vectors inclined at an angle of 120 °