koobas.hobune.stream
Vector Math - Linear Algebra
I am trying to make a connection in my linear algebra class! Here is a snippet from the textbook.
I am guessing this would be equivalent to new Vector3(2,3,3) ? Thanks in advance!
To translate that into Unity code, every Vector3 can be created using:
a*Vector3.right + b*Vector3.up + c*Vector3.forward
But there's no reason to do that. Your equation is part of the explanation of a basis for a space. It's explaining that those 3 vectors can make point, but they're just one option. In other words, they're not "the" axises - they're just one possible set.
this is all correct. fwiw, a basis of a vector space of dimension N (eg N = 3 for three dimensions) is any set of N vectors, which when normalized, each have a dot-product of magnitude strictly less than one with each other vector. ... that's just a mathy way of saying none of them are parallel or anti-parellel with each other. an "orthonormal" basis is a special case where the vectors are all mutually perpendicular and normalized. (because they're all mutually perpendicular, the dot products will all be zero) the "right", "up", and "forward" vectors form an orthonormal bases for ℝ3.
Sure - the OP has a textbook which I assume covers all of that. But the point is that the initial statement is a warm-up for the theory. It's not useful by itself, and isn't meant to be. It's like explaining binary math starting with a re$$anonymous$$der 93 is really 9*10+3.
yes. your answer was great, i'm not disagreeing with it in any way. i'm just adding a bit more info about basis vectors, since they came up. and yes the OP likely has a textbook covering them but that same textbook clearly left some room for doubt when it came to vector addition, so possibly having a different voice talk about basis vectors might help.
Discussion is the key word here. The main area of Unity Answers is for someone making something and one part of Unity doesn't seem to be working the way it says, and so on (the FAQ explains more.) The Help Room is for discussion, ... really a catch-all. Q's like this are now fine, but it would be nice if they were posted/moved out of default UA and into the Help Room (which I did right away, in this case, so no problems. But if any other Q seems more like a discussion, please more it to be nice to other users.)
Hello @FullHeartGames.
You are right on this one!
Thank you, just wanted to make sure I was thinking about it right, also it led to some interesting discussion!
