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In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
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.
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...
Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R 3. Consider the vectors e 1 = (1,0,0), e 2 = (0,1,0) and e 3 = (0,0,1). Then any vector in R 3 is a linear combination of e 1, e 2, and e 3. To see that this is so, take an arbitrary vector (a 1,a 2,a 3) in R 3, and write:
The y-intercept point (,) = (,) corresponds to buying only 4 kg of sausage; while the x-intercept point (,) = (,) corresponds to buying only 2 kg of salami. Note that the graph includes points with negative values of x or y , which have no meaning in terms of the original variables (unless we imagine selling meat to the butcher).
Force A points to the west and has a magnitude of 10 N and is represented by the vector <-10, 0>N. Force B points to the south and has a magnitude of 8.0 N and is represented by the vector <0, -8>N. Since these forces are vectors, they can be added by using the parallelogram rule [3] or vector addition.
A conical combination is a linear combination with nonnegative coefficients. When a point is to be used as the reference origin for defining displacement vectors, then is a convex combination of points ,, …, if and only if the zero displacement is a non-trivial conical combination of their respective displacement vectors relative to .
2. Types of Vectors • Zero Vector (\mathbf{0}): Magnitude is zero. • Unit Vector (\hat{A}): Magnitude is one. • Equal Vectors: Same magnitude and direction. • Negative Vector: Same magnitude but opposite direction. • Collinear Vectors: Parallel or anti-parallel vectors. • Coplanar Vectors: Lie in the same plane. 3. Operations on Vectors