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Vectors in Space
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Vector
An entity in space with both magnitude and direction, represented by an ordered list of numbers that define its position.
Dot Product
An algebraic operation that takes two equal-length sequences of numbers, usually vectors, and returns a single number.
Cross Product
A binary operation on two vectors in three-dimensional space which results in a vector that is perpendicular to the plane containing them.
Scalar Multiplication
Operation that multiplies a vector by a scalar (a single number), stretching or compressing its magnitude but not changing its direction.
Vector Addition
Putting two vectors together so that the resulting vector is derived from the sum of their individual components.
Unit Vector
A vector with a magnitude of one, used to denote direction without magnitude.
Magnitude of a Vector
The length or size of a vector represented as the square root of the sum of the squares of its components.
Basis Vectors
A set of vectors that, in linear combination, can represent every vector in a given vector space or coordinate system.
Orthogonal Vectors
Two vectors are orthogonal if their dot product is zero, which implies they are perpendicular to each other in space.
Linear Combination
A mathematical operation that combines multiple vectors using scalar multiplication and vector addition to create a new vector.
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