two vectors of equal magnitudes have a resulant equal to either of them .then the angle between then will be what
two vectors of equal magnitudes have a resulant equal to either of them .then the angle between then will be what
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Let the magnitude of the vectors = x
or |A| = x and |B| = x
Angle between the vectors = t
magnitude of resultant, |R| = x
|R|^2 = (|A|^2 + |B|^2 + 2|A||B| cos t)
=> x^2 = x^2 + x^2 + 2×x×x × cos t
=> x^2 = 2x^2 + 2x^2 cos t
=> x^2 = 2x^2( 1 + cos t )
=> x^2 / 2x^2 = 1 + cos t
=> 1/2 = 1 + cos t
=> 1/2 - 1 = cos t
=> -1/2 = cos t
=> cos t = -1/2 = cos (120°)
=> t = 120°
So angle between the vectors is 120°
Let the vectors be A and B.
Let the magnitude of the vectors = x
or |A| = x and |B| = x
Angle between the vectors = t
magnitude of resultant, |R| = x
|R|^2 = (|A|^2 + |B|^2 + 2|A||B| cos t)
=> x^2 = x^2 + x^2 + 2×x×x × cos t
=> x^2 = 2x^2 + 2x^2 cos t
=> x^2 = 2x^2( 1 + cos t )
=> x^2 / 2x^2 = 1 + cos t
=> 1/2 = 1 + cos t
=> 1/2 - 1 = cos t
=> -1/2 = cos t
=> cos t = -1/2 = cos (120°)
=> t = 120°
So angle between the vectors is 120°