we are given
[tex]a=i+3j-2k[/tex]
[tex]b=-i+5k[/tex]
we can find cross product
[tex]aXb=\begin{pmatrix}1&3&-2\end{pmatrix}\times \begin{pmatrix}-1&0&5\end{pmatrix}[/tex]
[tex]\mathrm{Computing\:cross\:product\:of\:two\:vectors}:\quad \left(u_1,\:u_2,\:u_3\right)\times \left(v_1,\:v_2,\:v_3\right)=\left(u_2v_3-u_3v_2,\:u_3v_1-u_1v_3,\:u_1v_2-u_2v_1\right)[/tex]
[tex]=\begin{pmatrix}3\times \:5-\left(-2\times \:0\right)&-2\left(-1\right)-1\times \:5&1\times \:0-3\left(-1\right)\end{pmatrix}[/tex]
[tex]aXb=15i-3j+3k[/tex]
