Question

if angle between a and b is π/3 , then angle between 2a and -3b is​

Answer 1

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

The magnitude of the two vectors are equal.

Hence, A = B.

The angle between vectors is given as 2\frac{\pi}{3}23π .

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\thetaR2= A2+B2+2ABcosθ

                         =A^2+A^2+2A^2cos\frac{2\pi}{3}=A2+A2+2A2cos32π

                         =2A^2+2A^2\times (-\frac{1}{2})=2A2+2A2×(−21)

                          =2A^2-A^2=2A2−A2        [  ∵  cos120=\frac{-1}{2}cos120=2−1  ]

                           =A^2=A2

                      ⇒ R=\ AR= A    [PROVED]