Re: Geometry: No four vectors can be pairwise at an right angle to each other


Hero wrote:
Randy Poe schrieb:
But vectors which are orthogonal under the the
dot product form right angles in the sense in which
Euclid defined them.
The other way round: vectors which form right angles in the sense
Euclid defined them are orthogonal under the dot product.

Both ways. Two vectors in R^n are orthogonal under the
vector dot product if and only if they form a right angle.

There is no such thing as vectors which are orthogonal
in that sense which do NOT form right angles. Is that
clear enough?

- Randy

.

Relevant Pages

  • Re: Geometry: No four vectors can be pairwise at an right angle to each other
    ... in that sense which do NOT form right angles. ... are common, the dot product resulting in a number (scalar), the vector ... [snip random word salad]. ...
    (sci.math)
  • Re: Geometry: No four vectors can be pairwise at an right angle to each other
    ... dot product form right angles in the sense in which ... in that sense which do NOT form right angles. ... consider the change of temperature with time at a certain locality. ... welche Elemente der Menge genannt werden, ...
    (sci.math)
  • Re: Component angles between 2 vectors
    ... each component (using dot product), and then do the same for V2... ... that you just have to compare the angles from V1 and the ones from V2 and... ... > I am attempting to determine the component angles of rotation between ... > the cos of the angle between them, and thus V1 rotated about this axis ...
    (microsoft.public.win32.programmer.directx.graphics)
  • Re: Making money from Java
    ... >>> With all due respect, Mr Wong, the Euclid I studied made ... >>> concluded that the sum of the angles of a triangle is equal to the sum ... > Propositions and the whole of these constitute the Geometry. ... the parallel line postulate says (or is ...
    (comp.lang.cobol)
  • Re: Triangle with more than 180 degrees-
    ... which is impossible in hyperbolic geometry. ... Then he defines a distance function as: ... but does not necessarily change angles, ... > which is defined upon the geometry of Euclid. ...
    (sci.math)