Question

resultant of two vectors of equal magnitude makes an angle 60 degree with one of the vectors .find the angle between the vectors

Answer 1

It is given that two vectors are having equal magnitude so the resultant must point midway among them.

The angle between the vectors will be 60 + 60 = 120.

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Answer 2

Answer:

120 degrees

Step-by-step explanation:

Let the angle between the vectors be α

it is given that angle between resultant and one vector is 60°

then tan 60 = $\frac{A sin\alpha }{A + A cos\alpha }$ = $\sqrt{3}$

---> $\sqrt{3}$ = $\frac{Asin\alpha }{A(1 + cos\alpha)}$

---> $\sqrt{3} (1 + cos\alpha) = sin\alpha$

--->$\sqrt{3} = sin\alpha -\sqrt{3} cos\alpha$

--->$\frac{\sqrt{3} }{2} = \frac{1}{2} sin\alpha - \frac{\sqrt{3} }{2} cos \alpha$       (dividing the whole equation by 2)

--->$sin 60 = cos 60 sin\alpha - sin 60 cos \alpha$

--->$sin 60 = sin (\alpha - 60)$

---> $60 = \alpha -60$

--->$\alpha$ = 60 +60 =120°