Question

Vector A has a magnitude of 4.00 units. Vector B has a magnitude of 7.10 units. The angle between A and B is 60.0 degrees. What is the magnitude of A+ B?

Answer 1

From the triangle $\triangle EFG$ using the cosine law, find the magnitude of $\vec{A} + \vec{B}$:

$$|\vec{A} + \vec{B}|^2 = A^2 + B^2 - 2AB\cos(180\degree - \theta)$$

where $A = |\vec{A}| = 4, B = |\vec{B}| = 7.1$, and $\theta = 60\degree$. Thus, obtain:

$$|\vec{A} + \vec{B}|^2 =4^2 + 7.1^2 - 2\cdot 4\cdot 7.1\cdot\cos120\degree =94.81$$

Thus

$$|\vec{A} + \vec{B}| = \sqrt{94.81} \approx 9.7$$

Answer. 9.7 units.