Multiplicação Escalar × Vetor
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
escala
About this calculator
The scalar-vector multiplication calculator performs the operation of multiplying a real number (scalar) by a vector. Given a scalar k and a vector v = (x, y), the result is a new vector where each component is multiplied by k: k·v = (k·x, k·y). This operation is fundamental in linear algebra and appears in many practical contexts.
The operation is simple: you enter the scalar value and the vector components (in two or three dimensions, depending on the calculator). The system then applies component-wise multiplication. For example, if k = 2 and v = (3, 4), the result is (6, 8). The calculator supports real numbers, including decimals and negatives.
Use this calculator when you need to resize a vector, such as in physics problems (force, velocity), computer graphics (scaling objects), or engineering (structural analysis). It is useful for students learning linear algebra or professionals who need quick and accurate calculations.
Cautions: ensure the scalar is a real number and the vector components are correct. Remember that multiplication by zero results in the zero vector. Also, in some applications, the scalar may represent a scale factor that should be positive to avoid direction reversal.
Frequently asked questions
What happens if I multiply a vector by zero?
The result is the zero vector (0, 0), regardless of the original vector's components.
Can I use negative numbers as scalars?
Yes, negative scalars reverse the direction of the vector and change its length proportionally.
Does the calculator work for three-dimensional vectors?
Yes, the calculator accepts vectors with two or three components. Just enter the values in the appropriate fields.
What is the difference between scalar multiplication and dot product?
Scalar multiplication combines a number and a vector, resulting in another vector. The dot product combines two vectors and results in a number.
How is scalar multiplication used in computer graphics?
It is used to scale objects, i.e., increase or decrease their size while maintaining proportion.