Vector c has a magnitude of 21.0 m and points in the −y‑ direction. vectors a and b both have positive y‑ components, and make angles of α=43.4° 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?

B=56.45 m

C=68.74 m

Explanation:

Analysis:

Because A + B + C = 0 the sum of the components of the vectors on the x and y axes must be equal to zero

Look at the attached figure

ΣFx=0

C*cos43.4 - B*cos27.7 = 0

C = B*cos27.7 ÷ cos43.4°

C = 1.2185B

ΣFy=0

C*sin43.4 - B*sin27.7 - A = 0 Equation (1)

We replace C = 1.2185B m and A = 21 m in the Equation (1):

1.2185B*sin43.4 - B*sin27.7 - 21 = 0

0.837B - 0.465B - 21 = 0

0.372B = 21

B = 21 ÷ 0.372

B = 56.45 m

C = 1.2185*56.45 m

C = 68.74 m

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