Vector A has a magnitude of 188 units and points30.0 o north of west. Vector B p

Question

Vector A has a magnitude of 188 units and points30.0o north of west. Vector B points50.0o east of north. Vector C points20.0o west of south. These three vectors add togive a resultant vector that is zero. Using components, findthe magnitudes of (a) vector B and (b) vector C. answer: (a) 371 units (b) 354 units Vector A has a magnitude of 188 units and points30.0o north of west. Vector B points50.0o east of north. Vector C points20.0o west of south. These three vectors add togive a resultant vector that is zero. Using components, findthe magnitudes of (a) vector B and (b) vector C. answer: (a) 371 units (b) 354 units

Explanation / Answer

First step is to break down the vector into components. Vector A: (188*cos(180-30))=-162.812 in x direction 188*sin(180-30)=94 in y direction Vector B: b*cos(90-50) = .766*b b*sin(90-50) = .643*b Vector C: c * cos(270-20) = -.342*c in x direction c * sin(270-20) = -.940*c in y direction Since the resultant is 0, we get a system of linear equations. -162.812+.766*b+-.342*c = 0 (we add the x components) 94+.643*b + -.940*c = 0 (we add the y components) Solve that system of equations using matrices, substitution or anyother method. I got the answers 370 and 353, but if you carry yourdecimals to a longer precision, your answer will be moreaccurate.

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