The DotProduct command computes the dot product of u and v.

The infix operator . can also be used to compute the dot product.

If u and v are $n$-dimensional Vectors, and conjugate is false, their dot product is given by the formula $\sum _{i=1}^n{u}_i{v}_i$. If conjugate is true, then their dot product is given by the formula $\sum _{i=1}^n\stackrel{\&conjugate0;}{u_i}{v}_i$.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right)\:$

$u≔⟨a\,b\,c⟩$

$u≔\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$

$v≔⟨d\,e\,f⟩$

$v≔\left[\begin{array}{c}d\\ e\\ f\end{array}\right]$

$\mathrm{`.`}\left(u\,v\right)$

$ad+be+cf$

$\mathrm{DotProduct}\left(u\,v\,\mathrm{conjugate}\=\mathrm{true}\right)$

$\stackrel{\&conjugate0;}{a}d+\stackrel{\&conjugate0;}{b}e+\stackrel{\&conjugate0;}{c}f$

$\mathrm{DotProduct}\left(v\,u\,\mathrm{conjugate}\=\mathrm{true}\right)$

$\stackrel{\&conjugate0;}{d}a+\stackrel{\&conjugate0;}{e}b+\stackrel{\&conjugate0;}{f}c$

The Student[MultivariateCalculus][DotProduct] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.