For \overrightarrow{a} = [0, 2, -3] and \overrightarrow{b} = [1, 1, 5]
a) Determine \overrightarrow{a} \times \overrightarrow{b}.
b) Show your work to confirm that \overrightarrow{a} \times \overrightarrow{b} is orthogonal to both \overrightarrow{a} and \overrightarrow{b}.