Vector C is 6.28 m long in a 105 degree direction. Vector D is 3.09 m long in a 233 degree direction. What is the magnitude and direction of their vector sum?

You can express the vectors in terms of their x - and y-components and add these components to receive the resulting vector.

vector C has components:

x = 6.28m * cos 105° = - 1.63m

y = 6.28m * sin 105° = 6.07m

vector D has components:

x = 3.09 * cos 233° = - 1.86m

y = 3.09 * sin 233° = - 2.47m

Adding both components to get the vector sum:

x = - 3.49m

y = 3.6m

You get the magnitude of the vector by using Pythagorean theorem:

magnitude = 5.01m

The angle ∅ is given by:

cos∅ = x/magnitude

Solving for ∅:

∅ = 134°