Category Geometry

The Pythagorean theorem (\( a^2 + b^2 = c^2 \)) is one of the cornerstones of geometry. It applies to every right triangle, where c is the hypotenuse (the side opposite the right angle) and a and b are the…

The scalar product(also called the dot product or inner product) is a fundamental operation in vector algebra. Given two vectors \(\vec{a}\) and \(\vec{b}\), their scalar product is defined both geometrically as \(\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta\) and algebraically via component-wise…