These numerous mathematical resources (calculators, quizzes, games, exercises, reminders, formulas) allow you to master the practice of vector calculation.

Vectors : Reminder

Coordinates of a vector from two points

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.

Directing vector of a line

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.

Coordinates of the midpoint of a segment

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

Distance between two points

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 .

Dot product

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.

Cross product

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.

Scalar triple product

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.

Determinant of two vectors (2x2)

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.

Determinant of three vectors (3x3)

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.