Bagels and Coffee, or, the vector dot product and you

I’ve been boning up on my math lately.
Like most TA’s I’ve cobbled together a bag of tricks from different situations I’ve dealt with over the years, but I’ve never really gone back to shore up my shaky high school trigonometry and pre-calculus. It’s certainly possible (at least, I hope it is!) to be a good TA with only seat-of-the-pants math skills — after all, we have parenting and scaling and all the other cool tricks in our apps to do the heavy lifting for us. Still, I’ve been finding that paying more attention to the math fundamentals is helping me solve problems more efficiently and elegantly than my patented hack-and-slash techniques did.
So, I’m starting an occasional series on some basic math concepts that I hope will be useful to other TA’s. I know it’s been helpful to me - there’s nothing that concentrates the mind like putting something out there on the internet for public commentary - it’s really forces you to think things through… At least, as long as you’re not on Twitter.