Displacement vectors A, B, and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 25.6° north of east. Vector B has a direction of 41.0° east of south, and vector C has a direction of 35.1° north of west. Find the magnitudes of vector B and vector C.

B = 5626.77 m

C = 6220. 5 m

Explanation:

Because the sum of the vectors must be equal to zero, then the result force in x and the result force in y must be zero.

We propose 2 equations x-y to solve the problem:

Rx : resulting from forces at x

Ry: resulting from forces at y

Rx = Ax+Bx+Cx=0

Ry = Ay+By+Cy=0

Ax = 1550 * cos25.6° = 1397.84

Ay = 1550 * sin25.6° = 669.73

Bx = B*sin41° = 0.656B

By = - B*cos41° = - 0.7547 B

Cx = - C*cos35.1° = - 0.8181 C

Cy = C * sin35.1° = 0.575 C

Rx = 1397.84+0.656B-0.8181 C=0

Ry = 669.73-0.7547 B + 0.575 C=0

System of 2 equations with 2 incognites:

+0.656B-0.8181 C = - 1397.84

-0.7547 B + 0.575 C = - 669.73

Resolving the system:

B = 5626.77 m

C = 6220. 5 m