A selection of free math resources (calculators, exercises, games, quizzes, course reminders) that teach the techniques of vector calculus.

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 coordinate calculator
allows you to do this type of calculation.

If, in a system, a line D has equation `y=m*x+p` then the vector `vecu(1;m)` is a **directing vector** of D.

The midpoint of [AB] has coordinates `((x_(a)+x_(b))/2;(y_(a)+y_(b))/2)` in the system (O,`vec(i)`,`vec(j)`).

The plane is provided with an orthonormal system (O,`vec(i)`,`vec(j)`) .
If A and B are two points with coordinates (`x_(a)`,`y_(a)`) and (`x_(b)`,`y_(b)`) in the (O,`vec(i)`,`vec(j)`) system,
then the **distance** AB is equal to:

AB=`sqrt((x_(b)-x_(a))^2+(y_(b)-y_(a))^2)`, the distance AB is also the **norm of the vector** `vec(AB)`, hich can be calculated using the
vector norm calculator
.

In the plan, in an orthonormal system `(O,vec(i),vec(j))` ,
`vec(u)` is a vector of coordinates (x,y) and `vec(v)` is a vector of coordinates (x',y'),
the **dot product** is given by the formula
xx'+yy'.

The
dot product calculator
allows this type of calculation for n-dimensional vectors.

In an orthonormal coordinate system (O,`vec(i)`,`vec(j)`,`vec(k)`), the **cross product**
of vectors `vec(u)(x,y,z)` and `vec(v)(x',y',z')` has coordinates `(yz'-zy',zx'-xz',xy'-yx')`, it notes `vec(u)^^vec(v)`.

This product can be determined using
cross product calculator.

The **scalar triple product** of three vectors `(vec(u),vec(v),vec(w))` is the number `vec(u)^^vec(v).vec(w)`.
In other words, the **scalar triple product** is obtained by calculating the
cross product
of `vec(u)` and `vec(v)` noted `vec(u)^^vec(v)`, then performing the dot product
dot product
of the vector `vec(u)^^vec(v)` and the vector `vec(w)`.
It can be calculated using the
scalar triple product calculator.

In an orthonormal coordinate system (O,`vec(i)`,`vec(j)`) , the vector `vec(u)` has coordinates (x,y)
(`vec(i)`,`vec(j)`), the vector `vec(v)` has coordinates (x',y'). The **determinant** of `vec(u)` et `vec(v)` is given by the
**formula xx'-yy'**.

This
example shows a calculation of the determinant of the vectors [[3;12];[45;2]] performed with the 2x2 determinant calculator.

Note: When the determinant of two vectors is zero, the two vectors are collinear.

In an orthonormal coordinate system (O,`vec(i)`,`vec(j)`,`vec(k)`), the vector `vec(u)` has coordinates (x,y,z)
, the vector `vec(v)` has coordinates (x',y',z'), the vector `vec(k)` has coordinates (x'',y'',z'').
The **determinant** of `vec(u)`, `vec(v)`, `vec(k)` is given by the **formula xy'z''+x'y''z+x''yz'-xy''z'-x'yz''-x''y'z**.

- cross_product : cross product calculator. The vector calculator allows the calculation of the cross product of two vectors online from their coordinates.
- determinant : determinant calculator. The determinant function calculates online the determinant of vectors or the determinant of a matrix.
- dot_product : Dot product calculator. The dot product calculator allows the calculation of the dot product of two vectors online from their coordinates.
- product_vector_number : product of a vector by a number. The vector calculator allows to calculate the product of a vector by a number online.
- scalar_triple_product : calculus scalar triple product. The scalar triple product calculator allows online calculation of scalar triple product.
- vector_calculator : vector calculator. The vector calculator allows to do calculations with vectors using coordinates.
- vector_coordinates : calculating the coordinates of a vector from two points.. The vector calculator allows the calculation of the coordinates of a vector from the coordinates of two points online.
- vector_difference : calculating the difference of two vectors. The vector_difference function is used to calculate the difference of two vectors online.
- vector_norm : calculating the norm of a vector. The vector calculator allows the calculation of the norm of a vector online.
- vector_sum : calculating the sum of two vectors. The vector calculator allows the calculation of the sum of two vectors online.

- Quiz on vectors (vectors): This quiz allows you to practice vector calculus: calculation of coordinates, norm, midpoint of a segment, dot product.

- Exercise 1524, ordinate of the direction vector of a line - vectors - equations - equations of lines and linear systems : The objective of this exercise is to determine the ordinate of a direction vector from a line equation.
- Exercise 3441, coordinates of a vector from the coordinates of two points - vectors : The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.
- Exercise 3442, calculation of the distance between two points - vectors : The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.
- Exercise 3443, calculation of the coordinates of the middle of a segment - vectors : The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.

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