Finding the length of a vector

In this publication, we will consider what the length of a vector is, how it is found, and also give an example of a task to demonstrate the application of theoretical knowledge in practice.

Determining the length of a vector

Length (or modulus) of a vector AB is a non-negative number that is equal to the distance between its start and end. In other words, this is the length of the corresponding segment AB.

For the considered vector, the length is denoted as |AB|, i.e. vertical lines are added on the sides.

Notes:

• Zero vector length 0, respectively, equals zero.
• Unit vector length e is equal to one.

Finding the length of a vector

Let’s say we have a vector a, which is given by its coordinates:

a = (a_x; to_y; to_z).

In this case, the length of the vector is calculated by the formula:

Thus, the length of a vector given by certain coordinates is equal to the square root of the sum of the squares of those coordinates.

Sample Tasks

Dan vector a = (2, -5, 6). Let’s find its length.

Solution

All we have to do is use the formula above and plug in the known values.