Question

the magnitude of two vectors are equal and the angle between them is theta. show that their resultant divides theta equally

Answer 1

we know that,
angle of resultant=tan^-1[(BSin theta)/(A+B Cos theta).
A=B let the angle is x.
hence proved.

Answer 2

Given:

The two vector a and b

The angles be Ф and ∅

The magnitude vector be A

To find:

The resultant theta that divides equally.

Solution:

We can start with tanФ

tanФ=bsin∅/a+bcos∅

As we take the magnitude a=b=A

Put back in above

tanФ=Asin∅/A+Acos∅

=sin∅/1+cos∅

As we know the different identities

sin∅=2sin(∅/2)cos(∅/2)

1+cos∅=2cos²∅/2

Putt back these values in the equation

tanФ=2sin(∅/2)cos(∅/2) / 2cos²∅/2

tanФ=sin(∅/2)/cos(∅/2)

tanФ=tan∅/2

Ф=∅/2

Hence the resultant angle divide the theta equallyФ=∅/2