Question

Two equal vectors have a resultant equal to either.The angle between them is what?

Answer 1

hey here is ur answer :

Two vectors of equal magnitude have a resultant equal to either of them. Then, the angle between them will be 2π/3 radians.

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Answer 2

Let the vectors be A and B and angle between them be alpha

Resultant = R

We know that A = B = R

$r = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha ) } \\ {a}^{2} = {a}^{2} + {a}^{2} + 2 {a}^{2} \cos( \alpha ) \\ {a}^{2} - 2 {a}^{2} = 2 {a}^{2} \cos( \alpha ) \\ 2 {a}^{2} \cos( \alpha ) = - {a}^{2} \\ \cos( \alpha ) = \frac{ - {a}^{2} }{2 {a}^{2} } = \frac{ - 1}{2} \\ \alpha = 120 {}^{o}$

120° = 2π/3 radian

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