I have been searching for an explanation in Howard's Linear Algebra and couldn't find an identical example to the one below.
The example tells me that vectors $\boldsymbol{a}_1$, $\boldsymbol{a}_2$ and $\boldsymbol{a}_3$ are:
$\boldsymbol a_1 = (a,0,0)$ $\boldsymbol a_2 = (0,a,0)$ $\boldsymbol a_3 = (0,0,a)$
And I have to calculate $\boldsymbol b_1$ using equation:
$\boldsymbol{b}_1 = \frac{2 \pi \, (\boldsymbol a_2 \times \boldsymbol a_3)}{(\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3)}$
So far I've only managed to calculate the cross product $(\boldsymbol a_2 \times \boldsymbol a_3)$ using Sarrus' rule and what I get is:
$\boldsymbol{b}_1 = \frac{2 \pi \, \hat{\boldsymbol{i}} \, a^2}{(\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3)}$
But now I am stuck as I don't know how to calculate with a $(\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3)$, as this is first time I've come across something like this.
Could you just point me to what to do next, or point me to a good html site as I still want to calculate this myself.
Best regards.