Indeed. And if they're cartesian vectors, you're good. But if that second number is an angle measured in radians, you use yet a different set of rules for the a

Indeed. And if they're cartesian vectors, you're good. But if that second number is an angle measured in radians, you use yet a different set of rules for the addition. The conversation with 16 year olds when you explain that their previous teacher who told them that you couldn't add points wasn't lying, but was, perhaps oversimplifying things to make their life easier, is a fun and fraught one. I've had to reason kids through the fact that a^2 + b^2 is not equal to (ab)^2 or even (a+b)^2 more times than I can count. What's particularly difficult is that, confronted with the fact that 25 and 49 are manifestly different numbers, many still cling to the rule that a^2 + b^2 = (a+b)^2, because of the "law of distribution", which they haven't learned as the "law of distribution of multiplication of monomials over addition, and only that".