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Vector Magnitude

Related Topics: More Lessons on Vectors

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


The length of a vector is called the magnitude or modulus of the vector.
magnitude of 2D 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.

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