My question concerns dot and cross products. I have no problem with vectors except in these two areas. I can _do_ the problems just fine, but I do not understand the point or see what is being accomplished or how it relates to anything we've been working on.
As for cross-products, their usefulness probably won't become apparent until we start studying torque and angular momentum, which is a few weeks down the road. However, dot products are a different story. Dot products are the most general way of finding the projection of one vector along the direction of another -- this is exactly what you must do to find the components of a vector (or vector equation). For example, when you find the x-component of a vector by taking the magnitude of the vector and multiplying by the cosine of the angle the vector makes with the x-axis, you are actually just taking the dot product of the vector and a unit vector in the +x-direction. We will make progressively more use of dot products as the quarter proceeds -- they will sometimes be used in analyzing free-body diagrams, and they will be used extensively when we discuss 'work' and energy. Little of what I discussed above should have been obvious to you -- the first few weeks of class have been spent making some basic definitions and introducing some math that will be important for the remainder of the quarter. You shouldn't be too bothered by the fact that things aren't (yet) especially synergetic.