Vector

Geometry Level 2

Two vectors have the same magnitude and start from the same point. The magnitude of their resultant is the same as the magnitude of one of the vectors. What is the angle between the two vectors?

120 ∘ {120}^\circ 180 ∘ {180}^\circ 45 ∘ {45}^\circ 60 ∘ {60}^\circ 90 ∘ {90}^\circ

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Nazmus Sakib
Sep 12, 2017

P 2 = P 2 + P 2 + 2 P 2 cos ⁡ α P^2 = P^2 + P^2 + 2P^2 \cos \alpha

or, P 2 = 2 P 2 ( 1 + c o s α ) P^2 = 2P^2 (1+\ cos \alpha)

or, P 2 2 P 2 = 1 + cos ⁡ α \dfrac{P^2}{2P^2} = 1+ \cos \alpha

or, 1 2 = 1 + cos ⁡ α \dfrac{1}{2} = 1 + \cos \alpha

or, 1 − 2 2 = cos ⁡ α \dfrac{1 - 2}{2} = \cos \alpha

or, ( − 1 2 ) = cos ⁡ α \left(-\dfrac{1}{2} \right) =\cos \alpha

or, α = cos ⁡ − 1 ( − 1 2 ) = 120 ∘ \alpha = \cos^{-1} \left(-\dfrac{1}{2} \right) = {120}^\circ

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