In these lessons, we will learn how to find the magnitude of 2-dimensional vectors and 3-dimensional vectors.

Related Topics: More Lessons on Vectors

The length of a vector is called the**magnitude** or modulus of the vector.

### Vectors in 2D

Vectors

Adding vectors geometrically, scalar multiplication, how to find the magnitude and direction angle of a vector.

A vector with initial point at the origin and terminal point at (a, b) is written <a, b>.

Geometrically, a vector is a directed line segment, while algebraically it is an ordered pair.

Example:

Find the magnitude and the direction angle for u = <-3, 4> Vectors : magnitude of a vector in 2D.

Example:

Find the magnitude of the following vectors:

a = 4i - 3j

b = -2i + 5j

### Vectors in 3D

A vector can also be 3-dimensional.

The following video gives the formula, and some examples of finding the magnitude, or length, of a 3-dimensional vector.

Examples:

Find the magnitude:

a = <3, 1, -2>

b = 5i -j + 2k Vectors : Magnitude of a vector 3D.

Examples:

1. Find the magnitude of a = 4i + 3j + 2k

2. If A(3, -5, 6) and B(4, 1, 3) find the length AB.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics: More Lessons on Vectors

The length of a vector is called the

** Example: **

Express each of the following vectors as a column vector and find its magnitude.

Adding vectors geometrically, scalar multiplication, how to find the magnitude and direction angle of a vector.

A vector with initial point at the origin and terminal point at (a, b) is written <a, b>.

Geometrically, a vector is a directed line segment, while algebraically it is an ordered pair.

Example:

Find the magnitude and the direction angle for u = <-3, 4> Vectors : magnitude of a vector in 2D.

Example:

Find the magnitude of the following vectors:

a = 4i - 3j

b = -2i + 5j

The following video gives the formula, and some examples of finding the magnitude, or length, of a 3-dimensional vector.

Examples:

Find the magnitude:

a = <3, 1, -2>

b = 5i -j + 2k Vectors : Magnitude of a vector 3D.

Examples:

1. Find the magnitude of a = 4i + 3j + 2k

2. If A(3, -5, 6) and B(4, 1, 3) find the length AB.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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