Multiply vector by the scalar online calculator

Multiplication of the vector and the scalar is called vector,

definition of the multiplication of the vector by the scalar

which has following properties:

Magnitude of the resulting vector equals to the product of the magnitude of the scalar and magnitude of the initial vector:

feature of vector by scalar multiplication

Vectors vector A and vector B, are codirectional, if α > 0 and oppositely directed, if α < 0.

product of the vector by the scalar


Product of the vector to the scalar also shares following properties:


associativity feature


distributivity feature

Distributivity relative to scalar:

distributivity relative to scalar feature

Input vector dimension

Vector dimension
Vector vector A representations form:
Vector vector A = { }
Vector vector A:

Input scalar

Scalar α =