Find u × v and show that it is orthogonal to both u and v.
$\begin{array} { l }
\mathbf { u } = \frac { 5 } { 7 } \mathbf { i } \
\mathbf { v } = \frac { 6 } { 7 } \mathbf { j } - 49 \mathbf { k }
\end{array}$
A) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = - 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { j } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
B) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = 35 \mathrm { i } - \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
C) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
D) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { j } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
E) $\begin{array} { l }
\mathbf { u } \times \mathbf { v } = 35 \mathbf { j } + \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$

Question

Find u × v and show that it is orthogonal to both u and v. 
 $\begin{array} { l } 
\mathbf { u } = \frac { 5 } { 7 } \mathbf { i } \
\mathbf { v } = \frac { 6 } { 7 } \mathbf { j } - 49 \mathbf { k }
\end{array}$
A) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = - 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { j } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
B) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = 35 \mathrm { i } - \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
C) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
D) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = 35 \mathbf { i } + \frac { 30 } { 49 } \mathbf { j } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$
E) $\begin{array} { l } 
\mathbf { u } \times \mathbf { v } = 35 \mathbf { j } + \frac { 30 } { 49 } \mathbf { k } \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \
( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0
\end{array}$

Quizplus · Accepted Answer

The cross product $\mathbf{u} \times \mathbf{v}$ results in a vector orthogonal to both $\mathbf{u}$ and $\mathbf{v}$. Given $\mathbf{u} = \frac{5}{7}\mathbf{i}$ and $\mathbf{v} = \frac{6}{7}\mathbf{j} - 49\mathbf{k}$, the cross product should have components in the $\mathbf{j}$ and $\mathbf{k}$ directions only, since $\mathbf{u}$ is in the $\mathbf{i}$ direction and $\mathbf{v}$ is in the plane formed by $\mathbf{j}$ and $\mathbf{k}$. The correct answer, therefore, involves a vector with $\mathbf{j}$ and $\mathbf{k}$ components, which is orthogonal to both $\mathbf{u}$ and $\mathbf{v}$, and this is satisfied by option E.

Find U × V and Show That It Is Orthogonal