Question

When the angle between two vectors of equal magnitude 2pi/3.prove that the magnitude of the resultant is equal to either?

Answer 1

let me know if it is right

Answer 2

Let us consider two vectors $\vec A\ and\ \vec B$ respectively.

The magnitude of the two vectors are equal.

Hence, A = B.

The angle between vectors is given as $2\frac{\pi}{3}$.

Let the magnitude of resultant of two vectors is R .

We have to prove that R = A = B

From parallelogram law of vector addition, we know that -

                        $R^2=\ A^2+B^2+2ABcos\theta$

                         $=A^2+A^2+2A^2cos\frac{2\pi}{3}$

                         $=2A^2+2A^2\times (-\frac{1}{2})$

                          $=2A^2-A^2$        [  ∵  $cos120=\frac{-1}{2}$  ]

                           $=A^2$

                      ⇒ $R=\ A$    [PROVED]