Math Visualization List
Calculus
First Derivative Second Derivative Integration
Determinant
2x2 & 3x3 Determinants Cramer's Rule Permutations & Inversions Permutation Definition & Expansion Properties of Determinants: Row Operations Minors & Cofactors Two-Row Laplace Expansion Vandermonde Determinant
Matrix Operations
Matrix Addition, Subtraction & Scalar Multiplication Matrix Multiplication & Power Transpose, Determinant & Adjoint Inverse Matrix & Matrix Equations Elementary Transformations, Echelon & Canonical Form
Probability & Statistics
Conditional Probability, Independence & Total Probability Discrete Probability Distributions PMF & CDF 2D Random Vectors Conditional Probability Distributions Bayes' Theorem Numerical Characteristics of Random Variables Higher Moments & Covariance Matrix Law of Iterated Expectations Independence, Mean Independence & Uncorrelated Continuous Statistical Distributions
Vector Operations
Vector Addition, Subtraction & Scalar Multiplication Linear Combination, Span & Basis Matrices as Transformations Composition of Transformations 3D Linear Transformations Determinant Inverse, Column Space & Rank Cross-Dimensional Transformations Vector Angle Cross Product Change of Basis Eigenvectors & Eigenvalues Function Vector Spaces Geometric Interpretation of Cramer's Rule Gravity Simulation

Vector Addition, Subtraction & Scalar Multiplication

Vector A (Red)

4
2

Vector B (Blue)

1
3

Real-time Calculation Results

Vector Magnitude
|A| = √(Ax² + Ay²)
|A| = 0
Vector B Magnitude
|B| = √(Bx² + By²)
|B| = 0
Dot Product
A · B = Ax×Bx + Ay×By
A · B = 0
Geometric meaning: |A||B|cos(θ)
Cross Product
A × B = Ax×By - Ay×Bx
A × B = 0
Geometric meaning: signed area of parallelogram
Angle Between Vectors
θ = arccos((A·B)/(|A||B|))
θ = 0°
Vector Sum
A + B = (Ax+Bx, Ay+By)
A + B = (0, 0)
|A + B| = 0
Tip:
The cross product in 2D represents the signed area of the parallelogram.
Vector A
Vector B
Result