3-vectors

set,get,print

• x,y,z - cartesian coordinates
• ,,z - cylindrical coordinates
• ,*,z
• r,, - spherical coordinates
• r,, - rapidity
• ,,
• direction cosines

working modes

• x,y,,z
• r,,

features

• +
• add or translate or move
• -
• *,dot - scalar product
• cross - vector product
• normalize
• scale
• rotate
• is_normalized

Other Notes

• Should it be possible to create underdefined vector ? For example, one sometimes knows x and y, but not z. Or should we than create 2-vector ? In that case we would need creations methods for transformations of 2-vectors and 3-vectors one to another (e.g. projections). I propose to use this possibility.
• Should we have angles ? We need one for rotate. But angles create many difficulties: What is for example the result of arcsine ? And there are more kinds of vectors - we need different treatment of and . Lets try to live without angles and see if it is possible.
• We need another class: direction. It is in principle the same as unit-vector (which I see as a vector without a length not a vector with a lenght equals to one). Than we can inherit the 3-vector from this direction.