what should be the angle between two vectors of same magnitude so that their resultant is equal to either of them?
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Answered by
11
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°
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°
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5
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