calculating the coordinates of a vector from two points.

The vector calculator allows to determine the coordinates of a vector from two points, it applies to points in the plane and space. The vector calculator returns the calculation steps.

Calculate the coordinates of a vector from two points in the plane

Let (O, `vec (i)`, `vec (j)`) a system, A and B two points which are respective coordinates (`x_a`,`y_(a)`) and (`x_(b)`,`y_(b)`) in the system (O,`vec(i)`,`vec(j)`) .

The coordinates of the vector `vec(AB)` are (`x_(b)`-`x_(a)`,`y_(b)`-`y_(a)`) in the system (O,`vec(i)`,`vec(j)`).

The vector calculator is able to calculate numeric coordinates or symbolic coordinates.

Let A(1;2) B(3;5) to calculate the coordinates of the vector `vec(AB)`, enter vector_coordinates(`[1;2];[3;5]`).

Let A(a;b) B(2*a;`b/2`) to calculate the coordinates of the vector `vec(AB)`, enter vector_coordinates(`[a;b];[2*a;b/2]`).

Calculate the coordinates of a vector from two points in space

Let (O,`vec(i)`,`vec(j)`,`vec(k)`) a system, A and B two points which are respective coordinates (`x_a`,`y_(a)`,`z_(a)`) and (`x_(b)`,`y_(b)`,`z_(a)`) in the system (O,`vec(i)`,`vec(j)`,`vec(k)`) .

The coordinates of the vector `vec(AB)` are (`x_(b)`-`x_(a)`,`y_(b)`-`y_(a)`,`z_(b)`-`z_(a)`) in the system (O,`vec(i)`,`vec(j)`,`vec(k)`).

The vector calculator allows to calculate numeric coordinates or symbolic coordinates.

Let A(1;2;1) B(3;5;2) to calculate the coordinates of the vector `vec(AB)`, enter vector_coordinates(`[1;2;1];[3;5;2]`) , the results [2;3;1] is returned.

Let A(a;b,c) B(2*a;2-b,c+1) to calculate the coordinates of the vector `vec(AB)`, enter vector_coordinates(`[a;b;c];[2*a;2-b;c+1]`) , the result [a;2-2*b;1] is returned.

Calculate the coordinates of a vector from 2 points in a system of any dimension

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