Vector Calc
Dot and cross products, norms, angles, projections, and parallelogram area for vectors in 2D or 3D.
About this tool
Choose the operation, enter its needed vectors, then Calculate. Unary norms/units use only their selected vector; scaling uses u and k. Binary operations require equal dimensions. Cross product is 3D; parallelogram area works in any dimension. Angles are returned in degrees. Projection projᵥ(u) is u projected onto the direction v; the scalar component retains its sign.
Use spaces or commas between dot-decimal components, or semicolons for individual components with decimal point/comma. Parentheses or square brackets are accepted. Empty separator cells are invalid. Up to 1024 components and 50000 characters; exponent notation supported. Result vectors use semicolons and can be pasted back. Small settings restore without automatic computation; edits clear old results.
Scaled normalization and compensated sums avoid common norm/product overflow. The angle uses unit-vector differences/sums rather than acos near parallel directions. Zero direction vectors make units/angles/target projections undefined; norm and distance remain defined. Float64, ten displayed significant digits. Extreme relative scales/cancellation can still lose precision; unrepresentable results return errors, not NaN/Infinity.