Find U × V and Show That It Is Orthogonal $\mathbf { u } = ( 13,1,14 ) \quad \mathbf { v } = ( 12 , - 12 , - 1 )$

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\mathbf { u } = ( 13,1,14 ) \quad \mathbf { v } = ( 12 , - 12 , - 1 )$

A) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 181,167 , - 167 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
B) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 181,167 , - 168 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0\end{array}$
C) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 167,181,168 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
D) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 167,181 , - 168 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
E) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 167,181 , - 168 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0\end{array}$