Help on vectors

[Guest]

Two tugboats are towing a loaded barge down the columbia river. Tugboat A has components 4i+J and tugboat B has components 2i-j. Find the angle between the two tugboats and the magnitude of the resultant force between them. How do I find the angle and magnitude?

[Guest]

angle is [tex]\cos\theta=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{a}\right|\left|\vec{b}\right|}[/tex]

magnitude is simple [tex]\left|\vec{a}+\vec{b}\right|=\left|4\hat{i}+\hat{j}+2\hat{i}-\hat{j}\right|=\left|6\hat{i}\right|=\boxed{6}[/tex]