Returns the scalar multiplication of s and v.

An overloaded version for the VectorCalculus package that deals with scaling Vectors (scalar multiplication) in different coordinate systems.

The following table describes the interaction between different types of Vector objects in different coordinate systems when the Star operator is applied.

Note that in 2-D math, the Star operator appears as a dot.

$\mathrm{with}\left(\mathrm{VectorCalculus}\right)\:$

$2⟨1\,1\,2⟩$

$\left(2\right)e_x\+\left(2\right)e_y\+\left(4\right)e_z$

$\mathrm{v1}≔\mathrm{Vector}\left(⟨1\,2⟩\,\mathrm{coordinates}=\mathrm{cartesian}\left[x,y\right]\right)$

$\mathrm{v1}≔\left[\begin{array}{c}1\\ 2\end{array}\right]$

$3\mathrm{v1}$

$\left(3\right)e_x\+\left(6\right)e_y$

$\mathrm{v2}≔\mathrm{RootedVector}\left(\mathrm{root}=\left[1\,\frac{\mathrm{\pi }}{2}\right]\,\left[1\,2\right]\,\mathrm{polar}\left[r,t\right]\right)$

$\mathrm{v2}≔\left[\begin{array}{c}1\\ 2\end{array}\right]$

$3\mathrm{v2}$

$\left[\begin{array}{c}3\\ 6\end{array}\right]$

$\mathrm{v3}≔\mathrm{RootedVector}\left(\mathrm{root}=\left[1\,2\right]\,\left[1\,1\right]\,\mathrm{parabolic}\left[u,v\right]\right)$

$\mathrm{v3}≔\left[\begin{array}{c}1\\ 1\end{array}\right]$

$2\mathrm{v3}$

$\left[\begin{array}{c}2\\ 2\end{array}\right]$

$\mathrm{vf}≔\mathrm{VectorField}\left(⟨x\,y⟩\,\mathrm{cartesian}\left[x,y\right]\right)$

$\mathrm{vf}≔\left(x\right){\stackrel{\_}{e}}_x\+\left(y\right){\stackrel{\_}{e}}_y$

$x\mathrm{vf}$

$\left(x^2\right){\stackrel{\_}{e}}_x\+\left(xy\right){\stackrel{\_}{e}}_y$

$\mathrm{pv}≔\mathrm{PositionVector}\left(\left[p\,p\right]\,\mathrm{polar}\left[r,t\right]\right)$

$\mathrm{pv}≔\left[\begin{array}{c}p\cos \left(p\right)\\ p\sin \left(p\right)\end{array}\right]$

$\frac{1}{2}\mathrm{pv}$

$\left[\begin{array}{c}\frac{p\cos \left(p\right)}{2}\\ \frac{p\sin \left(p\right)}{2}\end{array}\right]$