Do me a **favor**, take a few seconds to have a look at my last project.

Thank you, **Lulu**

The dot product (scalar product) of two vectors is the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product of vectors \(\vec{V}\) and \(\vec{U}\) can be calculated thanks to the following formula:

$$ \vec{V} \cdot \vec{U} = V_x.U_x + V_y.U_y + V_z.U_z = | \vec{V} |. | \vec{U} | .cos (\theta) $$

where \(\theta\) is the angle between \(\vec{V}\) and \(\vec{U}\).

If \(\vec{V}\) and \(\vec{U}\) are perpendicular, \(\vec{V} \cdot \vec{U}\) is equal to zero. |

If \(\vec{V}\) is null, \(\vec{V} \cdot \vec{U}\) is equal to zero. |

If \(\vec{U}\) is null, \(\vec{V} \cdot \vec{U}\) is equal to zero. |

\(\vec{V} \cdot \vec{V} = | \vec{V} | ^2\) |

\(\vec{V} \cdot \vec{U} = \vec{U} \cdot \vec{V}\) |

\(\vec{V} \cdot (-\vec{U}) = (-\vec{V}) \cdot \vec{U} = - ( \vec{V} \cdot \vec{U} )\) |

```
/*!
* \brief Compute the dot product of two vectors (this . V)
* The current vector is the first operand
* \param V is the second operand
* \return the dot product between the current vector and V
*/
inline double rOc_vector::dot(const rOc_vector V)
{
return this->x()*V.x() + this->y()*V.y() + this->z()*V.z();
}
```

- Calculating the transformation between two set of points
- Check if a number is prime online
- Check if a point belongs on a line segment
- Cross product
- Common derivatives rules
- Common derivatives
- How to check if four points are coplanar
- Common integrals (primitive functions)
- Least square approximation with a second degree polynomial
- Online square root simplifyer
- Sines, cosines and tangeantes of common angles
- Singular value decomposition (SVD) of a 2×2 matrix
- Tangent line segments to circles
- Understanding covariance matrices

Last update : 04/13/2019