This free online calculator help you to find a product of a vector by a scalar.

Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find a product of a vector by a scalar.

Calculator

Guide

Some theory

Scalar-vector multiplication calculator

Dimension of a vector:
Form of vector representation:

Input vector:

= {,

,

}

· a

Guide - scalar-vector multiplication calculator

To find the product of a vector by a scalar:

Select the vector dimension and the vector form of representation;

Type the coordinates of the vector;

Type a scalar (a real number or fraction) and press the button "=" and you will have a detailed step-by-step solution.

Entering data into the scalar-vector multiplication calculator

You can input only integer numbers or fractions in this online calculator. More in-depth information read at these rules.

Additional features of the scalar-vector multiplication calculator

You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard.

Theory. Scalar-vector multiplication

Geometric interpretation

The product of non-zero vector by the number is a vector collinear with given (codirectional given if the number is positive, having the opposite direction if the number is negative) and its magnitude is equal to the module of the vector multiplied by the module of number.

Algebraic interpretation

The product of non-zero vector by the number is a vector which coordinates are equal to the corresponding coordinates of the vector, multiplied by the number.

In the case of the 3d problem the product of vector a = {a_{x} ; a_{y} ; a_{z}} by the number k can be found using the following formula: