Find U × V and Show That It Is Orthogonal $\begin{array} { l } \mathbf { u } = - \mathbf { i } + \mathbf { k } \\\mathbf { v } = \mathbf { j } - 3 \mathbf { k }\end{array}$

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\begin{array} { l } \mathbf { u } = - \mathbf { i } + \mathbf { k } \\\mathbf { v } = \mathbf { j } - 3 \mathbf { k }\end{array}$

A) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = \mathbf { i } - 3 \mathbf { j } - \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
B) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = - \mathbf { i } - 3 \mathbf { j } - \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
C) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = - \mathbf { i } + 3 \mathbf { j } - \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
D) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = - \mathbf { i } - 3 \mathbf { j } + \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
E) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = \mathbf { i } - 3 \mathbf { j } + \mathbf { k } \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$