calculating the norm of a vector

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.