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) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = ( 0,0,30 ) \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0
\end{array}$

Question

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) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = ( 0,0,30 ) \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0
\end{array}$

Quizplus · Accepted Answer

The cross product $\mathbf{u} \times \mathbf{v}$ is calculated using the determinant of a matrix formed by the unit vectors $\mathbf{i}, \mathbf{j}, \mathbf{k}$ and the components of $\mathbf{u}$ and $\mathbf{v}$. The result, $(0,30,0)$, is orthogonal to both $\mathbf{u}$ and $\mathbf{v}$ as their dot products with $(0,30,0)$ are zero, confirming the properties of the cross product.

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

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