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Vectors in Space

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Vector Addition

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Putting two vectors together so that the resulting vector is derived from the sum of their individual components.

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Vector

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An entity in space with both magnitude and direction, represented by an ordered list of numbers that define its position.

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Unit Vector

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A vector with a magnitude of one, used to denote direction without magnitude.

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Basis Vectors

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A set of vectors that, in linear combination, can represent every vector in a given vector space or coordinate system.

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Dot Product

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An algebraic operation that takes two equal-length sequences of numbers, usually vectors, and returns a single number.

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Scalar Multiplication

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Operation that multiplies a vector by a scalar (a single number), stretching or compressing its magnitude but not changing its direction.

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Cross Product

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A binary operation on two vectors in three-dimensional space which results in a vector that is perpendicular to the plane containing them.

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Magnitude of a Vector

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The length or size of a vector represented as the square root of the sum of the squares of its components.

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Linear Combination

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A mathematical operation that combines multiple vectors using scalar multiplication and vector addition to create a new vector.

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Orthogonal Vectors

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Two vectors are orthogonal if their dot product is zero, which implies they are perpendicular to each other in space.

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