Vector Magnitude

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

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Equal Vectors
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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 .

Magnitude Vector

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

Vectors in 2D

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.

Find the magnitude and the direction angle for u = <-3, 4>

Vectors: magnitude of a vector in 2D.

Find the magnitude of the following vectors:
a = 4i - 3j
b = -2i + 5j

Vectors in 3D

The following diagram shows how to find the magnitude of a 3D Vector.
Magnitude of 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.

Find the magnitude:
a = <3, 1, -2>
b = 5i -j + 2k

Vectors : Magnitude of a vector 3D.


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

Try the free Mathway calculator and problem solver below to practice various 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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