# calculating the norm of a vector

## Calculus vector_norm

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### Function : vector_norm

#### Summary :

The vector calculator allows the calculation of the norm of a vector online.

Vector_norm online

#### Description :

The vector calculator allows to determine the norm of a vector from the coordinates. Calculations are made in exact form , they may involve numbers but also letters . The norm of a vector is also called the length of a vector.

# Calculate the norm of a vector in the plane

Let (O,vec(i),vec(j)) an orthonormal frame of the plan, the vector vec(u) has coordinates (x,y) in the basis (vec(i),vec(j)), the norm of vec(u) is equal to sqrt(x^2+y^2)

The vector calculator is able to calculate the norm of a vector knows its coordinates which are numeric or symbolic.

Let vec(u)(1;1) to calculate the norm of vector vec(u), enter vector_norm([1;1]) , after calculating the norm is returned , it is equal sqrt(2).

Let vec(u)(a;2) to calculate the norm of vector vec(u), type vector_norm([a;2]) , after calculating, the result sqrt(a^2+4) is returned.

# Calculating the norm of a vector in space

Let (O,vec(i),vec(j),vec(k)) an orthonormal frame of the space, the vector vec(u) has coordinates (x,y,z) in the basis (vec(i),vec(j),vec(k)), the norm of vec(u) is equal to sqrt(x^2+y^2+z^2).

The vector calculator allows to calculate the norm of a vector knows its coordinates which are numeric or litteral.

Let vec(u)(1;1;1) to calculate the norm of vector vec(u), enter vector_norm([1;1;1]) , after calculating the norm is returned , it is equal sqrt(3).

Let vec(u)(a;2;1) to calculate the norm of vector vec(u), enter vector_norm([a;2;1]) , after calculating the result sqrt(5+a^2) is returned.

# Calculating the norm of a vector in a space of any dimension

The vector calculator is used according to the same principle for calculating the norm of a vector in a space of any dimension.

The vector calculator allows the calculation of the norm of a vector online.

#### Syntax :

vector_norm(vector)

#### Examples :

vector_norm([1;1]), returns sqrt(2)

Calculate online with vector_norm (calculating the norm of a vector)