Operations with vectors – What is it, definition and concept

The mathematical operations that can be applied to the coordinates of vectors are addition, subtraction, and multiplication by a scalar.

In other words, the mathematical operations that can be done on the coordinates of vectors are addition, subtraction, and multiplication by a number.

vector addition

To add two or more vectors, we will have to add the coordinates in such a way that the axis for each coordinate of the vectors coincides. The first coordinate corresponds to the X axis and the second coordinate corresponds to the Y axis. Then we will have to operate the coordinates that coincide on the axis. Schematically:

  • The x-linked coordinates for the following vectors are the “a” coordinate for vector v and the “c” coordinate for vector x.
  • The Y-axis coordinates for the following vectors are the “b” coordinate for vector v and the “d” coordinate for vector x.

The new vector will be the sum of the following vectors or it can also be defined as a new vector:

vector addition
vector addition

The sum of the vectors will be the sum of their coordinates respecting the axis to which they belong. We can see how the first coordinate of the sum vector is the sum of the first coordinates of the vectors (a and c). The second coordinate of the vector sum is the sum of the second coordinates of the vectors (b and d).

Vector Subtraction

To subtract two or more vectors, we will have to subtract the coordinates so that the axis of each coordinate of the vectors coincides.

The first coordinate corresponds to the X axis and the second coordinate corresponds to the Y axis. Then we will have to operate the coordinates that coincide on the axis. Schematically:

  • The x-linked coordinates for the following vectors are the “a” coordinate for vector v and the “c” coordinate for vector x.
  • The Y-axis coordinates for the following vectors are the “b” coordinate for vector v and the “d” coordinate for vector x.

The new vector will be the subtraction of the following vectors or it can also be defined as a new vector:

Vector Subtraction
Vector Subtraction

The subtraction of the vectors will be the subtraction of their coordinates respecting the axis to which they belong. We can see how the first coordinate of the subtraction vector is the subtraction of the first coordinates of the vectors (a and c). The second coordinate of the subtraction vector is the subtraction of the second coordinates of the vectors (b and d).

Multiplication by a scalar

The multiplication of a vector by a number (scalar) is completed by doing the product of said number by the coordinates of the vector. The new vector will be the multiplication of the vector by the scalar or it can also be defined as a new vector:

Multiplication by a scalar
Multiplication by a scalar

Example of operations with vectors

Add, subtract, and multiply by a scalar the following vectors:

Example
Example
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