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  2. Vector projection - Wikipedia

    en.wikipedia.org/wiki/Vector_projection

    The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b ⁡ a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .

  3. Tangential and normal components - Wikipedia

    en.wikipedia.org/wiki/Tangential_and_normal...

    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.

  4. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    Typically, these components are the projections of the vector on a set of mutually perpendicular reference axes (basis vectors). The vector is said to be decomposed or resolved with respect to that set. Illustration of tangential and normal components of a vector to a surface. The decomposition or resolution [16] of a vector into components is ...

  5. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.

  6. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    For vectors with complex entries, using the given definition of the dot product would lead to quite different properties. For instance, the dot product of a vector with itself could be zero without the vector being the zero vector (e.g. this would happen with the vector = [ ]).

  7. Trace (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Trace_(linear_algebra)

    The components of this vector field are linear functions (given by the rows of A). Its divergence div F is a constant function, whose value is equal to tr( A ) . By the divergence theorem , one can interpret this in terms of flows: if F ( x ) represents the velocity of a fluid at location x and U is a region in R n , the net flow of the fluid ...

  8. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:

  9. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    Both the use of symbols and the naming order of tuple coordinates differ among the several sources and disciplines. This article will use the ISO convention [1] frequently encountered in physics, where the naming tuple gives the order as: radial distance, polar angle, azimuthal angle, or (,,). (See graphic re the "physics convention".)