Math Vectors Study Cards

Enhance Your Learning with Math Vectors Flash Cards for quick learning



Vector

A quantity that has both magnitude and direction.

Magnitude

The length or size of a vector.

Direction

The orientation or angle of a vector.

Addition

The operation of combining two vectors to form a resultant vector.

Subtraction

The operation of finding the difference between two vectors.

Scalar Multiplication

The operation of multiplying a vector by a scalar, resulting in a vector with changed magnitude.

Dot Product

The operation of multiplying two vectors to obtain a scalar quantity.

Cross Product

The operation of multiplying two vectors to obtain a vector perpendicular to both.

Projection

The process of finding the component of a vector in a particular direction.

Decomposition

The process of breaking down a vector into its component vectors.

Equations

Mathematical expressions that describe the relationship between vectors.

Calculus

The branch of mathematics that deals with rates of change and accumulation.

Fields

Regions of space where a vector quantity is defined at every point.

Geometry

The branch of mathematics that deals with shapes, sizes, and properties of figures and spaces.

Algebra

The branch of mathematics that deals with symbols and the rules for manipulating those symbols.

Visualization

The process of representing vectors graphically to aid understanding.

Notation

The system of symbols used to represent vectors and vector operations.

Transformations

Operations that change the position, orientation, or size of vectors.

Matrices

Arrays of numbers used to represent vectors and perform vector operations.

Spaces

Sets of vectors that satisfy certain properties and operations.

Analysis

The branch of mathematics that deals with limits, continuity, and infinite series.

Calculations

The process of performing mathematical operations on vectors.

Quantities

Physical properties that can be represented by vectors, such as force, velocity, and acceleration.

Magnitude and Direction

The two components that fully describe a vector.

Components and Operations

The parts and actions involved in working with vectors.

Algebraic Properties

The rules and relationships that govern vector operations.

Applications in Physics

The use of vectors to describe and analyze physical phenomena.

Applications in Engineering

The use of vectors in designing and building structures and systems.

Applications in Computer Science

The use of vectors in algorithms, data structures, and computer graphics.

Applications in Mathematics

The use of vectors in mathematical modeling and problem-solving.

Applications in Economics

The use of vectors in economic analysis and optimization.

Applications in Biology

The use of vectors in biological research and modeling.

Applications in Chemistry

The use of vectors in chemical reactions and molecular structures.

Applications in Medicine

The use of vectors in medical imaging and biomechanics.

Applications in Geology

The use of vectors in studying Earth's structure and processes.

Applications in Astronomy

The use of vectors in celestial mechanics and astrophysics.

Applications in Robotics

The use of vectors in robot motion planning and control.

Applications in Artificial Intelligence

The use of vectors in machine learning and pattern recognition.

Applications in Data Science

The use of vectors in analyzing and interpreting large datasets.

Applications in Machine Learning

The use of vectors in training and evaluating machine learning models.

Applications in Image Processing

The use of vectors in enhancing and analyzing digital images.

Applications in Signal Processing

The use of vectors in analyzing and manipulating signals.

Applications in Communication Systems

The use of vectors in transmitting and receiving information.

Applications in Control Systems

The use of vectors in regulating and optimizing system behavior.

Applications in Optimization

The use of vectors in finding the best solution to a problem.