Question

two vectors of equal magnitudes have a resulant equal to either of them .then the angle between then will be what

Answer 1

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°

Answer 2

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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°