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Topic: Cross product

Related Topics

Triple product

Dot product

Evaluating cross products

Wedge product

Inner product space

Biquaternion

Quaternions and spatial rotation

Product rule

Vector fields in cylindrical and spherical coordinates

Vector space

Vector field

Rotation group

Lorenz force

Divergence

Vector calculus

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	Math Tutorial -- Cross Product
		As illustrated in figure 11.1, the cross product of two vectors is perpendicular to the plane defined by these vectors.
		Note that the magnitude of the cross product is zero when the vectors are parallel or anti-parallel, and maximum when they are perpendicular.
		This contrasts with the dot product, which is maximum for parallel vectors and zero for perpendicular vectors.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node112.html (275 words)

	Vectors, Part 7
		The applet shows the cross product of the green vector with the yellow vector (in that order) as the red vector, and all three vectors are also projected onto the xy-plane.
		The cross product of v and w is a vector that is perpendicular to both v and w and has length equal to v
		The length of the cross product is also the area of the parallelogram determined by the two vectors.
	www.math.duke.edu /education/ccp/materials/mvcalc/vectors/vec4.html (879 words)

	Cross product
		In mathematics, the cross product is a binary operation on vectors in three dimensions.
		The cross product is also used to describe the Lorenz force[?] experienced by a moving electrical charge in a magnetic field.
		A cross product for 7-dimensional vectors can be obtained in the same way by using the octonions instead of the quaternions.
	www.ebroadcast.com.au /lookup/encyclopedia/cr/Cross_product.html (668 words)

	PlanetMath: cross product (Site not responding. Last check: 2007-11-07)
		is a vector orthogonal to the plane of the two vectors being crossed, whose magnitude is equal to the area of the parallelogram defined by the two vectors.
		The cross product produces the vector that would be in a right-handed coordinate system with the plane.
		This is version 42 of cross product, born on 2001-11-15, modified 2006-09-13.
	planetmath.org /encyclopedia/CrossProduct.html (333 words)

	PlanetMath: triple cross product (Site not responding. Last check: 2007-11-07)
		The cross product of a vector with a cross product is called the triple cross product.
		Note that the use of parentheses in the triple cross products is necessary, since the cross product operation is not associative, i.e., generally we have
		This is version 25 of triple cross product, born on 2004-03-16, modified 2006-03-15.
	planetmath.org /encyclopedia/VectorTripleProduct.html (200 words)

	Cross product - CGAFaq
		Historically, the cross product was defined (separately) by Josiah Willard Gibbs and Oliver Heaviside as a portion of the quaternion product, useful for physical applications (such as Maxwell's theory of electromagnetism).
		Although, properly speaking, the cross product exists only in 3D, an occasional abuse of terminology is to refer to the “cross product” of planar vectors, a scalar result that can be interpreted as the z component of a vector in the xy plane.
		For example, the cross product of two vectors is the zero vector if they are collinear, or perpendicular to their common plane if they are independent.
	cgafaq.info /wiki/Cross_Product (446 words)

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