Where \ cdot denotes the dot product and { \ mathbf { w } } the ( not necessarily normalized ) normal vector to the hyperplane.
42.
By dividing the normal vector \ vec n by its magnitude | \ vec n |, we obtain the unit ( or normalized ) normal vector
43.
By dividing the normal vector \ vec n by its magnitude | \ vec n |, we obtain the unit ( or normalized ) normal vector
44.
One, you continue to add the force normal vectors between each sheet in order to claim " we have PRECISELY the same normal force ".
45.
Solving these local extremum principles for hyperbolic LCSs in two and three dimensions yields unit normal vector fields to which hyperbolic LCSs should everywhere be tangent.
46.
Thus the normal vector space and the normal affine space have dimension 1 and the normal affine space is the " z "-axis.
47.
In three dimensions it is the same as the angle between the normal vectors dual to the planes, and it generalises to some extent in higher dimensions.
48.
It can be shown From its dependence on volume forms for its definition we see that the affine normal vector field is invariant under volume preserving affine transformations.
49.
A plane is given by a normal vector \ vec n as well as an arbitrary position vector \ vec a of a point A \ in E.
50.
M _ \ infty is the freestream Mach number, and n _ x, n _ y, n _ z are the surface-normal vector components.
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