Vector C has a magnitude of 24.6 m and points in the − y ‑ direction. Vectors A and B both have positive y ‑ components, and make angles of α = 44.9 ° and β = 27.7 ° with the positive and negative x - axis, respectively. If the vector sum A + B + C = 0 , what are the magnitudes of A and B ?

A= 61.35

B= -44.40

Explanation:

1. Using the components method we have:

Considering that the vector sum , then:

Then:

It means the value of x and y component is 0.

2. Determinate the equations that describe each component:

Form Eq. (1):

Replacing A in Eq. (2):

Replacing values of C, α and β in (4):

Replacing value of B in (3)

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