# 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.

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| =

(x

- to calculate the length of a vector in two-dimensional space _{B}- x_{A})^{2}+ (y_{B}- y_{A})^{2}|AB| =

(x

- to calculate the length of a vector in three-dimensional space_{B}- x_{A})^{2}+ (y_{B}- y_{A})^{2}+ (z_{B}- z_{A})^{2}In order to find the modulus (length) of a vector, if its coordinates are known, you must use one of the formulas.

|ฤ| =

a

- to calculate the length of a vector in two-dimensional space _{x}^{2}+ a_{y}^{2}|ฤ| =

a

- to calculate the length of a vector in three-dimensional space _{x}^{2}+ a_{y}^{2}+ a_{z}^{2}**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| =

(x

=_{B}- x_{A})^{2}+ (y_{B}- y_{A})^{2}(4 - 1)

=^{2}+ (7 - 9)^{2}3

=^{2}+ (-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| =

(x

=_{B}- x_{A})^{2}+ (y_{B}- y_{A})^{2}+ (z_{B}- z_{A})^{2}(3 - 5)

=^{2}+ (6 - 2)^{2}+ (7 - 9)^{2}(-2)

=^{2}+ 4^{2}+ (-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

a

_{x}= 3;

a

_{y}= 8;

Substitute the values into the formula and find the modulus of the vector ฤ

|ฤ| =

a

=_{x}^{2}+ a_{y}^{2}3

=^{2}+ 8^{2}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

a

_{x}= 4;

a

_{y}= 2;

a

_{y}= 7;

Substitute the values into the formula and find the modulus of the vector ฤ

|ฤ| =

a

=_{x}^{2}+ a_{y}^{2}+ a_{z}^{2}4

=^{2}+ 2^{2}+ 7^{2}16 + 4 + 49

=69

= 8.30662386291807