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In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.
The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted or a ⊥b), [1] is the orthogonal projection of a onto the plane (or, in general, hyperplane) that is orthogonal to b.
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 term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the ...
n is a unit vector perpendicular to the plane containing a and b, with direction such that the ordered set (a, b, n) is positively oriented. If the vectors a and b are parallel (that is, the angle θ between them is either 0° or 180°), by the above formula, the cross product of a and b is the zero vector 0.
As a result, the unit binormal vector = is perpendicular to the xy-plane and thus must be either ,, or ,, . By the right-hand rule B will be 0 , 0 , 1 {\displaystyle \langle 0,0,1\rangle } if, when viewed from above, the curve's trajectory is turning leftward, and will be 0 , 0 , − 1 {\displaystyle \langle 0,0,-1\rangle } if it is turning ...
A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length.
Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2. (F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c. The line L is called the reflection axis or the associated mirror.
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.