${\mathbf{U}}_2\times {\mathbf{U}}_3\= \|\begin{array}{ccc}\mathbf{i}& \mathbf{j}& \mathbf{k}\\ 2& 5& -4\\ 5& 7& 6\end{array}\|$ = $\left[\begin{array}{c}58\\ -32\\ -11\end{array}\right]$

${\mathbf{U}}_3\times {\mathbf{U}}_1\=\|\begin{array}{ccc}\mathbf{i}& \mathbf{j}& \mathbf{k}\\ 5& 7& 6\\ 3& -2& 4\end{array}\|$ = $\left[\begin{array}{c}40\\ -2\\ -31\end{array}\right]$

${\mathbf{U}}_1\times {\mathbf{U}}_2\=\|\begin{array}{ccc}\mathbf{i}& \mathbf{j}& \mathbf{k}\\ 3& -2& 4\\ 2& 5& -4\end{array}\|$ = $\left[\begin{array}{c}-12\\ 20\\ 19\end{array}\right]$

${\mathbf{V}}_1\=\frac{1}{194}$ $\left[\begin{array}{c}58\\ -32\\ -11\end{array}\right]$

${\mathbf{V}}_2\=\frac{1}{194}\left[\begin{array}{c}40\\ -2\\ -31\end{array}\right]$

${\mathbf{V}}_3\=\frac{1}{194}\left[\begin{array}{c}-12\\ 20\\ 19\end{array}\right]$

Initialize

Loading Student:-MultivariateCalculus

Enter the vectors ${\mathbf{U}}_1\,{\mathbf{U}}_2\,{\mathbf{U}}_3$ 

$⟨3\,-2\,4⟩$$\stackrel{\text{assign to a name}}{\to }$$U_1$

$⟨2\,5\,-4⟩$$\stackrel{\text{assign to a name}}{\to }$$U_2$

$⟨5\,7\,6⟩$$\stackrel{\text{assign to a name}}{\to }$$U_3$

Compute $\mathrm{\λ}\=\left[{\mathbf{U}}_1{\mathbf{U}}_2{\mathbf{U}}_3\right]$ 

${\mathbf{U}}_1\,{\mathbf{U}}_2\,{\mathbf{U}}_3$ = $\stackrel{\text{scalar triple product}}{\to }$$194$$\stackrel{\text{assign to a name}}{\to }$$\mathrm{\λ}$

Obtain the reciprocal vectors as per the formulas in Table 1.5.1 

Display the reciprocal vectors

${\mathbf{V}}_1\,{\mathbf{V}}_2\,{\mathbf{V}}_3$

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

${\mathbf{U}}_1\,{\mathbf{U}}_2\,{\mathbf{U}}_3≔⟨3\,-2\,4⟩\,⟨2\,5\,-4⟩\,⟨5\,7\,6⟩\:$

$\mathrm{\λ}≔\mathrm{BoxProduct}\left({\mathbf{U}}_1\,{\mathbf{U}}_2\,{\mathbf{U}}_3\right)\:$

$$\begin{gathered} {\mathbf{V}}_1≔\mathrm{CrossProduct}\left({\mathbf{U}}_2\,{\mathbf{U}}_3\right)\/\mathrm{\λ}\: \\ {\mathbf{V}}_2≔\mathrm{CrossProduct}\left({\mathbf{U}}_3\,{\mathbf{U}}_1\right)\/\mathrm{\λ}\: \\ {\mathbf{V}}_3≔\mathrm{CrossProduct}\left({\mathbf{U}}_1\,{\mathbf{U}}_2\right)\/\mathrm{\λ}\: \end{gathered}$$

Display the reciprocal vectors

${\mathbf{V}}_1\,{\mathbf{V}}_2\,{\mathbf{V}}_3$