Scalar products (also known as dot or inner products) are the simplest form of multiplication between two vectors. There are two complementary definitions for the scalar product of two vectors [math]\vec{v}[/math] and [math]\vec{w}[/math].[br][br]The first is in terms of the vector components [math]v_{k}[/math] and [math]w_{k}[/math], where [math]k\in\mathbb{N}[/math]:[br][math]\vec{v}\cdot\vec{w}=\sum_{i=1}^{k}{v_{i}w_{i}}[/math][br][br]The second uses the magnitudes of and angle between [math]\vec{v}[/math] and [math]\vec{w}[/math]:[br][math]\vec{v}\cdot\vec{w}=\left|\vec{v}\right|\left|\vec{w}\right|\cos\theta[/math]

How is the projection of [math]\vec{v}[/math] onto [math]\vec{w}[/math] related to the scalar product of [math]\vec{v}[/math] and [math]\vec{w}[/math]?[br][br]How about for the projection of [math]\vec{w}[/math] onto [math]\vec{v}[/math]?