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In math, a "vector field" is an abstract term for a set, and a number of operations, that have specific properties. Matrices of the same size, for example, all 3 x 2 matrices, combined with matrix addition and multiplication by a scalar, happens to have all those properties. You may want to read an introductory Linear Algebra book for more details.
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What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
Can a vector be less than its magnitude?
For a start, you can't compare a vector with a scalar, so you can't really compare a vector with its magnitude, either. To say which is larger, you can't even compare one vector with another - you can only compare their magnitudes.
What are the applications of vector algebra and vector calclus?
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
What is the difference between unit vectors and column vectors?
a unit vector is any vector with length or absolute value 1. A column vector is any vector written in a column of since we say an mxn matrix is m rows and n columns, a column vector is mx1 matrix.
