Vector A has a magnitude of 188 units and points 30.0 degrees north of west. Vec

Question

Vector A has a magnitude of 188 units and points 30.0 degrees north of west. Vector B points 50.0 degrees east of north. Vector C points 20.0 degrees west of south. These three vectors add to give a resultant vector that is zero. Using components method, find the magnitude of (a) vector B and (c) Vector C Vector A has a magnitude of 188 units and points 30.0 degrees north of west. Vector B points 50.0 degrees east of north. Vector C points 20.0 degrees west of south. These three vectors add to give a resultant vector that is zero. Using components method, find the magnitude of (a) vector B and (c) Vector C

Explanation / Answer

vector A = 188 (- cos30i + sin30j) = - 162.82i + 94j

vector B = B (sin50i + cos50j) = 0.766Bi + 0.643Bj

vector C = C ( - sin20i - cos20 j) = -0.342Ci - 0.940C j

Resultant vector = vector A + vector B + vector C

0 = (-162.82 + 0.766B - 0.342C)i + (94 + 0.643B - 0.940C)j

0.766B - 0.342C = 162.82

-0.643B + 0.940C = 94

Solving,

B = 370.3 units

C = 353.3 units

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