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A normal vector of length one is called a unit normal vector. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by −1 results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior).
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.
One may wish to express rotation as a rotation vector, or Euler vector, an un-normalized three-dimensional vector the direction of which specifies the axis, and the length of which is θ, = ^. The rotation vector is useful in some contexts, as it represents a three-dimensional rotation with only three scalar values (its components ...
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
T is the unit vector tangent to the curve, pointing in the direction of motion. N is the normal unit vector, the derivative of T with respect to the arclength parameter of the curve, divided by its length. B is the binormal unit vector, the cross product of T and N.
A direction is often represented as a unit vector, the result of dividing a vector by its length. A direction can alternately be represented by a point on a circle or sphere, the intersection between the sphere and a ray in that direction emanating from the sphere's center; the tips of unit vectors emanating from a common origin point lie on ...
A direction in (n + 1)-dimensional space will be a unit magnitude vector, which we may consider a point on a generalized sphere, S n. Thus it is natural to describe the rotation group SO(n + 1) as combining SO(n) and S n. A suitable formalism is the fiber bundle, (+),
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.