Two quick questions: 1. Are two vectors considered collinear if the angle between them is 180°? (My guess would be yes, but it can't hurt to double check) 2. Let's say you're given a problem like this: "given A = (1, 2, 3) and B = (x, 5, 6), find the value of x such that A and B are collinear" The first method that comes to mind is to recognize that the cosine of the angle between the two has to be 1 (or -1 as well, depending on the answer to my first question), and from there using the definition of the dot product to conclude that A dot B = |A||B|. However, using this method, you have now turned what appears to be a reasonably straightforward problem into one that involves using the quadratic equation and generates an extraneous solution, requiring you to check both values to determine which one is actually valid. Is there a simpler way to solve a problem like that, or is there no choice but to do all of that ugly algebra?