How about this for a polynomial time solution : first do what was suggested above, find the nearest point on the plane to the origin, and find its hyper-octant by taking the sign of each vector component.
32.
Model a bunch of bouncing balls under a constant force of gravity, but make all the collisions elastic ( i . e . flip all the vector components the opposite sign when it hits a wall or another ball ).
33.
Since these operations are common in application, all vector components in this section are presented with respect to the normalised basis : F _ i = \ mathbf { F } \ cdot \ hat { \ mathbf { e } } _ i.
34.
Each orbital in an atom is characterized by a unique set of values of the three quantum numbers,, and, which respectively correspond to the electron's energy, angular momentum, and an angular momentum vector component ( the magnetic quantum number ).
35.
If a displacement or velocity vector is separated into its vector components, then the horizontal part will be positive for motion to the right and negative for motion to the left, while the vertical part will be positive for motion upward and negative for motion downward.
36.
Here, XS and YS represent the sign bits of the movement vectors, XV and YV indicate an overflow in the respective vector component, and LB, MB and RB indicate the status of the left, middle and right mouse buttons ( 1 = pressed ).
37.
Now I know probably few people do always bother; my question is more asking if there are certain times ( ie when dealing with vector components ) when writing the arrow would be improper . Preceding talk ) 21 : 02, 7 August 2008 ( UTC)
38.
For nonlinear molecules which are symmetric rotors ( or symmetric tops-see next section ), there are two moments of inertia and the energy also depends on a second rotational quantum number, K, which defines the vector component of rotational angular momentum along the principal symmetry axis.
39.
However, applying this expansion to each vector component of or will give solutions that are not generically divergence-free ( "' " "'?"'B "'0 } } ), and therefore require additional restrictions on the coefficients.
40.
Geometrically, such a transformation takes pairs of points in a linear space, that are purely axially separated along the axis whose row in the matrix contains the shear element, and effectively replaces those pairs by pairs whose separation is no longer purely axial but has two vector components.
