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

**Related Pages**

Vectors

Equal Vectors

Vector Multiplication

Vector Geometry

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

The following diagram shows the magnitude of a vector. Scroll down the page for more
examples and solutions to calculate the magnitude of 2-D and 3-D vectors .

**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 diagram shows how to find the magnitude of a 3D Vector.

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.

**Example:**

Find the magnitude:

a = <3, 1, -2>

b = 5i -j + 2k

Vectors : Magnitude of a vector 3D.

**Examples:**

- Find the magnitude of a = 4i + 3j + 2k
- If A(3, -5, 6) and B(4, 1, 3) find the length AB.

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