Analytic geometry

Vectors

Magnitudes, dot and cross products, angles and projections.

Analytic geometry

2D vector magnitude

|a| = √(x²+y²)→
Analytic geometry

3D vector magnitude

|a| = √(x²+y²+z²)→
Analytic geometry

Vector dot product

a·b = aₓbₓ+aᵧbᵧ+a₂b₂→
Analytic geometry

Cross product magnitude

|a×b| = √((aᵧb₂−a₂bᵧ)²+…)→
Analytic geometry

Angle between vectors

θ = arccos((a·b)/(|a||b|))→
Analytic geometry

Scalar vector projection

comp_b a = (a·b)/|b|→
Analytic geometry

Vector addition

a + b→
Analytic geometry

Vector subtraction

a − b→
Analytic geometry

Vector cross product

a × b→