# calculating the sum of two vectors

## Calculus vector_sum

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### Function : vector_sum

#### Summary :

The vector calculator allows the calculation of the sum of two vectors online.

vector_sum online

#### Description :

The vector calculator allows to determine the sum of two vectors of the plane or space.

# Calculate the sum of two vectors of the plan

Let (O,vec(i),vec(j)) a frame of the plan, vec(u) and vec(v) two vectors that have the respective coordinates (x_u,y_(u)) and (x_(v),y_(v)) in the frame (O,vec(i),vec(j)) .

The vector vec(u+v) has coordinates (x_(u)+x_(v),y_(u)+y_(v)) in the system (vec(i),vec(j)).

The vector calculator is able to add vectors that have numeric or literal coordinates.

Lets vec(u)(1;2) vec(v)(3;5) to calculate the sum vec(u)+vec(v), enter vector_sum([1;2];[3;5]) , after calculation the vector [4;7] is returned.

Lets vec(u)(a;b) vec(v)(2*a;b) to calculate the sum vec(u)+vec(v), enter vector_sum([a;b];[2*a;b])

# Calculate the sum of two vectors in space

Let (O,vec(i),vec(j),vec(k)) a space frame, vec(u) and vec(v) two vectors that have the respective coordinates (x_u,y_(u),z_(u)) and (x_(v),y_(v),z_(v)) in the frame (O,vec(i),vec(j),vec(k)) .

The vector vec(u+v) has coordinates (x_(u)+x_(v),y_(u)+y_(v),z_(u)+z_(v)) in the system (vec(i),vec(j),vec(k)).

The vector calculator is able to add vectors that have numeric or literal coordinates.

Lets vec(u)(1;2;1) vec(v)(3;5;2) to calculate the sum vec(u)+vec(v), enter vector_sum([1;2;1];[3;5;2]) after calculation, the result [4;7;3] is returned.

Lets vec(u)(a;b,c) vec(v)(2*a;2-b,c+1) to calculate the sum vec(u)+vec(v), enter vector_sum([a;b;c];[3*a;2;2*c+1]) , after calculation, the result [a;2-2*b;1] is returned.

# Calculate the sum of two vectors in a space of any dimension

The vector calculator is used according to the same principle for any dimension of spaces.

The vector calculator allows the calculation of the sum of two vectors online.

#### Syntax :

vector_sum(vector;vector)

#### Examples :

vector_sum([1;1;1];[5;5;6]), returns [6;6;7]

Calculate online with vector_sum (calculating the sum of two vectors)