>> In fact, a proper vector in physics has 4 features: point of >> application, magnitude, direction and sense. >> > > No -- a vector has the properties "magnitude" and direction. > Although not everything that has magnitude and direction is a > vector. > > It's very unusual to have a fixed point of application as a vector's > property (at least I haven't seen it so far). That would complicate > equality tests. > Interesting. It appears that we are ran into a mathematical cultural difference. Were I come from vectors *are* defined as having four properties that I enumerated. After some research I found that English sources (Wikipedia) indeed give the definition you supplied. In my old mechanics textbook (which is in English) vectors are divided into 'fixed' (having a clearly defined point of application), 'sliding' (p.o.a. can be moved along a line) and 'free' (those not associated with a unique line in space).
However, given the following problem: (assuming 2-d Cartesian coordinate system and gravity acting 'downwards') "There are 3 point masses: 2 kg at (0, 0), 1 kg at (5, 4) and 4 kg at (2, 2). The acting forces are given as vectors: [2, 2] [1, 1]. Find the trajectories of all point masses." how would you propose to solve it without knowing where the forces are applied? >> In case of a vector in two dimensions (a special case, which you >> also fail to stress not to mention that you were talking about >> space) the magnitude and sense can be described by one number > > Actually, the "magnitude" and "sense" you use here are redundant. > What's the difference between a vector with magnitude "1" and > sense "-", and magnitude "-1" and sense "+"? > Again, I think we were given different definitions. Mine states that direction is 'the line on which the vector lies', sense is the 'arrow' and magnitude is the 'length' (thus non-negative). The definition is separate from mathematical description (which can be '[1 1] applied at (0, 0)' or 'sqrt(2) at 45 deg applied at (0, 0)' or any other that is unambiguous). >> and the direction as another. >> > > Represent the direction as one number? Only in a one-dimensional > space. > No. In one-dimensional 'space' direction is a ± quantity (a 'sense'). In 2-d it can be given as an angle. Regards, Greg -- http://mail.python.org/mailman/listinfo/python-list
