Instructions: select the correct answer.

vector u has a magnitude of 5 units and a direction angle of 30°. vector v has a magnitude of 7 units and a direction angle of 120°. what is the direction angle of their vector sum?

a.) 82.21°

b.) 84.46°

c.) 85.11°

d.) 86.13°

84.463°

Step-by-step explanation:

Determine the x- and y-components of these two vectors.  Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:

x-comps:

5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83

y-comps:

5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562

Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°:  ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or

1.474 rad       180°

*  =  84.463°

       1                π