Find U × V and Show That It Is Orthogonal $\mathbf { u } = ( 10,0,3 ) \quad \mathbf { v } = ( 10,0,0 )$

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\mathbf { u } = ( 10,0,3 ) \quad \mathbf { v } = ( 10,0,0 )$

A) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 0,30,0 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
B) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 0 , - 30,0 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
C) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 0,30,0 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0\end{array}$
D) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 30,0,0 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0\end{array}$
E) $\begin{array} { l } \mathbf { u } \times \mathbf { v } = ( 0,0,30 ) \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0\end{array}$