(A new question of the week) We were recently asked to check work on an interesting little question about parallel vectors, and I was almost convinced that there was no solution … until I realized there was one! How was it missed? How can we avoid doing that? That’s our goal today.
(A new question of the week) Here we have a different kind of question than usual: A conjecture about distances between points, with a request for confirmation. Normally we like to just give hints to help a student figure something out; this was a request for a theorem that ought to exist, and trying to …
A recent question about the resultant velocity of an airplane illustrates different ways to make a diagram showing the bearings of air velocity and wind velocity, and to work out angles without getting too dizzy.
(A new question of the week) Among many interesting recent questions we have one about vectors and equations in three dimensions. We’ll see four different ways to find the distance from a point to a line, proving two formulas and catching some of the errors one can make along the way. We’ll also see a …
(An archive question of the week) We’ve looked at the scalar (dot) product and the vector (cross) product; but there is one answer in the Ask Dr. Math archives that was too long to fit in either post. Here we’ll see again where the two familiar products come from, while looking deeper into the math …
Last time, we looked at the scalar, or dot, product of vectors, focusing on proving the equivalence of two ways to define it. This time, we’ll look at the vector, or cross, product in the same way. The distinction between dot and cross product reflects the symbol used, u · v vs. u × v, …
We’re looking at the concept of vectors at an introductory level. Last week we looked at how they are defined in this context (as quantities with magnitude and direction), and how they are added (which is really part of the definition). Our collection of answers from Ask Dr. Math this time focuses on the ideas …
Because we have had a number of questions about vectors recently, I thought it might be time to look at various facets of that topic. Here, we will start with some ideas about what vectors, and their most basic operations, are. Next week, we’ll get into the far more interesting topic of multiplying vectors.
A new question of the week We haven’t done much with vectors here, though there have been many problems of that sort lately. Let’s look at a recent question that touches on the basics, yet is by no means a simple problem.
(Archive Question of the Week) An interesting question that has been referred to many times since it was written in 1999 deals with averaging angles. At first the question seems trivial; then almost impossible; and then we end up with a rather simple formula that is totally unlike what we started with. And further applications …