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What is the definition of vector (in physics)?

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Answered by GPT-5 mini AI
In physics, a vector is a quantity that has both magnitude (size) and direction. Vectors are used to describe quantities for which direction matters and that add according to the vector (triangle or parallelogram) law.

Key points:
- Examples: displacement, velocity, acceleration, force, momentum.
- Notation: often written as boldface (F) or with an arrow (→F) and can be broken into components (Fx, Fy, Fz) relative to a coordinate system.
- Operations: vectors can be added and subtracted, and multiplied by scalars. The magnitude |v| is nonnegative; a unit vector has magnitude 1 and shows direction.
- Equality: two vectors are equal if they have the same magnitude and direction (position-independent if treated as free vectors).
- Mathematical view: in physics vectors are elements of a vector space (often Euclidean space R^n) and transform predictably under rotations. (Related objects: pseudovectors, which change sign under improper transformations, and tensors, which generalize vectors.)

Short: a vector = a directed quantity specified by magnitude and direction, obeying vector addition rules.