The solution is (v, u) = (- 585.709, 593,034). Please notice that the value of v only means that the direction of the real vector is antiparallel to the supposed one.
What are the magnitudes of two vectors to get the zero vector by vector sum?
According to the definition of vector sum and vectors in rectangular form, we must solve the following vector equation:
(0, 0) = 205 · (cos 23°, - sin 23°) + v · (- cos 75°, sin 75°) + u · (- cos 55°, - sin 55°)
(0, 0) = (188.703, 80.100) + v · (- 0.259, 0.966) + u · (- 0.574, 0.819)
(- 188.703, - 80.100) = v · (- 0.259, 0.966) + u · (- 0.574, 0.819)
Then, we must solve the following system of linear equations:
- 0.259 · v - 0.574 · u = - 188.703
0.966 · v + 0.819 · u = - 80.100
The solution is (v, u) = (- 585.709, 593,034). Please notice that the value of v only means that the direction of the real vector is antiparallel to the supposed one.
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