Dot product calculator
Dot product calculator
The dot product calculator allows the calculation of the dot product of two vectors online from their coordinates.
- Analytical definition of the scalar product
- Property
- Online calculation of the scalar product.
- Dot product calculation from numeric coordinates.
- Dot product calculation from literal coordinates.
It is possible to calculate the dot product of two vectors from their coordinates.
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'.
This definition can be extended to space. In a direct orthonormal system `(O,vec(i),vec(j),vec(k))`,
`vec(u)` is a vector of coordinates (x,y,z) and `vec(v)` is a vector of coordinates (x',y',z'),
the dot product is given by the formula
xx'+yy'+zz'.
If `vec(u)` and `vec(v)` are orthogonal, then the dot product is zero.
The dot product calculator allows to calculate the dot product of two vectors from their coordinates. The calculation of the scalar product online can be done with numbers or literal expressions.
To calculate the dot product of the following vectors `vec(v)` [1;5] and `vec(u)` [1;3], enter dot_product(`[1;5];[1;3]`). After calculation the result 16 is returned.
To calculate the dot product of the following vectors `vec(v)` `[a;b-1]` and `vec(u)` `[2a;a/2]`, enter dot_product(`[a;b-1];[2a;a/2]`). After calculation the result `-a/2+(b*a)/2+2*a^2` is returned.
Syntax :
dot_product(vector;vector)
Examples :
- Vector calculator : vector_calculator. The vector calculator allows to do calculations with vectors using coordinates.
- Calculating the coordinates of a vector from two points. : vector_coordinates. The vector calculator allows the calculation of the coordinates of a vector from the coordinates of two points online.
- Determinant calculator : determinant. The determinant function calculates online the determinant of vectors or the determinant of a matrix.
- Calculating the difference of two vectors : vector_difference. The vector_difference function is used to calculate the difference of two vectors online.
- Calculating the norm of a vector : vector_norm. The vector calculator allows the calculation of the norm of a vector online.
- Calculus scalar triple product : scalar_triple_product. The scalar triple product calculator allows online calculation of scalar triple product.
- Dot product calculator : dot_product. The dot product calculator allows the calculation of the dot product of two vectors online from their coordinates.
- Product of a vector by a number : product_vector_number. The vector calculator allows to calculate the product of a vector by a number online.
- Cross product calculator : cross_product. The vector calculator allows the calculation of the cross product of two vectors online from their coordinates.
- Calculating the sum of two vectors : vector_sum. The vector calculator allows the calculation of the sum of two vectors online.