Angle between two vectors of equal magnitude is 120 degrees prove that the magnitude of their resultant is - Physics - Motion In A Plane

Question

Angle between two vectors of equal magnitude is 120 degrees
prove that the magnitude of their resultant is equal to either of
them

123456789 · Accepted Answer

Let the 2 vectors be A and B and their resultant be R
To prove :- A=B=R
For an easier way, Let us use this relation to find out theta
when A=B=R
R^2 = A^2 + B^2 + 2ABCostheta
Here A^2 = B^2 = R^2 ,
Hence, R^2 = R^2 + R^2 + 2R^2 (Costheta)
R^2 = 2R^2 + 2R^2 (Costheta)
Cos theta = (R^2 - 2R^2) / 2R^2 = (-R^2) / 2R^2
Cos theta = -1/2
Hence theta = 120 degrees
Thus proved

Angle between two vectors of equal magnitude is 120 degrees . prove that the magnitude of their resultant is equal to either of them.