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Vector Modulus (Length) Calculator

Vector length calculator, gives a detailed solution and calculate the modulus of a vector in two-dimensional space and a vector in three-dimensional space.

Dimension of space
Specify the form of the vector

Specify the coordinates of the vector ฤ
ฤ = { ; }

How to Find the Modulus (Length) of a Vector in 2d and 3d Space

Vector module |AB| is called a number equal to the distance between the starting and ending points of the vector.
In order to find the modulus (length) of a vector, if the coordinates of its start and end points are known, you must use one of the formulas.
|AB| =
(xB - xA)2 + (yB - yA)2
- to calculate the length of a vector in two-dimensional space
|AB| =
(xB - xA)2 + (yB - yA)2 + (zB - zA)2
- to calculate the length of a vector in three-dimensional space

In order to find the modulus (length) of a vector, if its coordinates are known, you must use one of the formulas.
|ฤ| =
ax2 + ay2
- to calculate the length of a vector in two-dimensional space
|ฤ| =
ax2 + ay2 + az2
- to calculate the length of a vector in three-dimensional space

Example 1 , find the length of a vector in two-dimensional space with coordinates of the start and end points A (x; y) and point B (x; y), where A (1; 9) and B (4; 7).
Then according to the formula
Xb = 4;
Xa = 1;
Yb = 7;
Ya = 9;
Substitute the values into the formula and find the modulus of the vector |AB|
|AB| =
(xB - xA)2 + (yB - yA)2
=
(4 - 1)2 + (7 - 9)2
=
32 + (-2)2
=
9 + 4
=
13
= 3.60555127546399
Example 2 , find the length of a vector in three-dimensional space with coordinates of the start and end points A (x; y; z) and point B (x; y; z), where A (5; 2; 9) and B (3; 6; 7).
Then according to the formula
Xb = 3;
Xa = 5;
Yb = 6;
Ya = 2;
Zb = 7;
Za = 9;
Substitute the values into the formula and find the modulus of the vector |AB|
|AB| =
(xB - xA)2 + (yB - yA)2 + (zB - zA)2
=
(3 - 5)2 + (6 - 2)2 + (7 - 9)2
=
(-2)2 + 42 + (-2)2
=
4 + 16 + 4
=
24
= 2
6
= 4.89897948556636

Example 3 , find the length of the vector ฤ in two-dimensional space with coordinates ฤ (x; y), where ฤ (3; 8).
Then according to the formula
ax = 3;
ay = 8;
Substitute the values into the formula and find the modulus of the vector ฤ
|ฤ| =
ax2 + ay2
=
32 + 82
=
9 + 64
=
73
= 8.54400374531753

Example 4 , find the length of the vector ฤ in three-dimensional space with coordinates ฤ (x; y; z), where ฤ (4; 2; 7).
Then according to the formula
ax = 4;
ay = 2;
ay = 7;
Substitute the values into the formula and find the modulus of the vector ฤ
|ฤ| =
ax2 + ay2 + az2
=
42 + 22 + 72
=
16 + 4 + 49
=
69
= 8.30662386291807
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