Find U × V and Show That It Is Orthogonal

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $$\begin{array} { l } \mathbf { u } = 12 \mathbf { i } + 6 \mathbf { j } + \mathbf { k } \\\mathbf { v } = \mathbf { i } + 5 \mathbf { j } - 6 \mathbf { k }\end{array}$$

A) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } - 41 \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
B) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } + 73 \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
C) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } + 54 \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
D) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = - 41 \mathbf { i } + 73 \mathbf { j } + 54 \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
E) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = - 41 \mathbf { i } + 73 \mathbf { j } - 41 \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$