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