A has a length 3.76 cm and is at an angle of 34.5 degrees above the positive x-direction. B has a length 4.53 cm and is at an angle of 34.1 degrees above the negative x-direction. What is their sum?

If C = A + B, then:    C_x = A_x + B_x     C_y = A_y + B_y.

The resultant vector is: C = -0.65 cm + 4.67 cm

Or, express the resultant in terms of its magnitude and direction.

C² = C_x² + C_y² = 0.65² + 4.67²  or   C = 4.72 cm.

tan(θ)

=

4.67 -0.65

This gives θ = 97.9 degrees.

The resultant vector has magnitude 4.72 cm and is rotated 97.9 counterclockwise from the +x direction.