Two force vectors are oriented such that the angle between their directions is 46 degrees and they have the same magnitude. If their magnitudes are 2.81 newtons, then what is the magnitude of their sum

F = 5.17 N

Explanation:

If we know the magnitudes of both vectors, and the angle between them, we can find the magnitude of their sum, applying the cosine theorem, as follows:

       

Replacing by the givens, F₁ = F₂ = 2.81 N, θ = 46º, we get:

       

We can infer that star y is closer but other factors must be considered including the heat of the star, the mass, and the brightness of the star. even though star x seems dimmer it may just be less bright or contain less heat.