Ok, I work with 3D coordinate measuring systems every day, and often must calclulate vector I, J, K values using trig. But since I never took any calculus I must admit that I don't fully understand vectors.
I know that in my XYZ coordintate system 'I' is related to X, J is related to Y, and K is related to Z, and that the IJK values result in movement direction in a given axis, or axes.
Example, an IJK of 1, 0, 0 will move my point in the +X direction, or that an IJK of 0.707, 0, 0.707 will move my point at a +45° angle in my ZX plane.
But again, (and it may be obvious), I really don't understand what going on. Can anyone give me a quick Vectors 101?
The coordinate system you mention, the Cartesian system is, as you may realize only one of several. There are others such as polar coordinate. But vectors seek to quantify quantities that by their length represent magnitude and by their orientation, direction. As long as quantities are constant, they are capable of being calculated by graphic or trigonometric means. But, as you know, not all forces are constant, some things follow variable or curved paths. In order to calculate values that are changing the whole time, it is necessary to use calculus. That method breaks the curved line into infinitesimally small pieces and then sums, or integrates, the tiny little bits to arrive at a total. I'm sure that Professor, or methos, or someone else can explain the concept better, but I've been retired for almost 20 years and, frankly, I've forgotten almost everything I ever knew about both calculus and vector analysis. Actually, I suspect that most engineers and mathematicians probably do a lot of this stuff with hand held calculators nowadays. I belong to the slide rule era.
I'm not sure from your question what you aren't clear about.
Vectors are a direction and a distance/magnitude.
In ijk notation, imagine a starting point such as 0,0,0 in cartesian (x,y,z) space. Move i steps in x, j steps in y, and k steps in z. The straight-line distance between where you started and where you ended up is the magnitude. The direction of an arrow pointing from where you started to where you end up is the direction. The vector, really, is that arrow, which contains both the magnitude and direction.
ijk isn't the only way to represent vectors. You can also, for example, represent it directly as 2 angles (one left-right, one up-down) and a distance. This style might be simpler for understanding what a vector really is, but it makes calculation more difficult in cartesian space, since you can't just add to find your final location.
Kendor, the good news is you don't have to know any calculus to understand vectors -- just a little algebra. And if you understand trig, then applying trig to vectors is fairly straightforward -- think geometrically and make lots of diagrams. (After you learn basic calculus you can move on to vector calculus -- but that's a whole different animal.) In fact, from the examples you already gave it sounds like you understand it better than you realize!
It might help to ask specific questions or post a specific problem or two. Good luck.
Ah, the slide rule era! Electronic calculators weren't invented until after I finished my undergraduate degree in physics, so I got to be good with my Post Versalog. No, I didn't dangle it from my belt but I did keep a 6" "pocket slide rule" in my glove compartment to compute gas mileage. As old-time engineers are fond of saying, "We sent men to the moon using slide rules."
Posts: 1895 | Location: U.S. | Registered: 06-03-02
You old-timers like Juan and Prof, I sold my log.log decitrig, with leather case on eBay a couple of years ago. As I recall I think I got about $40.00 for it. Probably an antique collector ?
For the last couple of years we've been downsizing. Went from a four bedroom house to a two bedroom apartment. I know the slide rule didn't take up a lot of room, but in an auction you have no,idea how high the bidding might take something. I sold a wheelbarrow for more than I had paid for it the previous year, and an artificial tree for a shipping cost that was more than a brand new one would have cost. Go figger!
As old-time engineers are fond of saying, "We sent men to the moon using slide rules."
