Fundamental Concepts: Vectors

These flashcards cover vocabulary and key concepts related to vectors as presented in the lecture notes.

Vector

A quantity having direction as well as magnitude.

Scalar

A physical quantity that has magnitude only and is completely described by a single number.

Euclidean Space

A three-dimensional space characterized by a set of three numbers (x, y, z) relative to an origin.

Unit of Length

A standard measurement taken as one ten-millionth of a quadrant of Earth's meridian, later defined as a distance light travels in a specific time.

Cyclical System

A system used to measure time based on the reoccurrences of certain natural phenomena, like the swinging of a pendulum.

Dimensional Analysis

A method used to analyze relationships between physical quantities by identifying their dimensions.

Null Vector

A vector with a magnitude of zero, denoted by (0,0,0).

Magnitude of a Vector

The length of a vector, calculated as the square root of the sum of the squares of its components.

Transformation Matrix

A matrix that represents a linear transformation from one coordinate system to another.

Dot Product

A scalar product defined for two vectors A and B, given by A·B = AxBx + AyBy + Az*Bz.

Cross Product

A vector product that results in a vector that is perpendicular to the plane formed by the two original vectors.

Polar Coordinates

A system of coordinates where a point in the plane is determined by a distance from a reference point and an angle from a reference direction.

Velocity

The rate of change of the position vector of a particle with respect to time, often represented as $v = \frac{dr}{dt}$ where $r$ is the position vector.

Acceleration

The rate of change of the velocity vector with respect to time, given by $a = \frac{dv}{dt}$ where $v$ is the velocity vector.