Find a unit vector orthogonal to u and v. $\begin{array} { l }
\mathbf { u } = \mathbf { i } + \mathbf { j } \
\mathbf { v } = \mathbf { j } + \mathbf { k }
\end{array}$
A) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( - \mathbf { i } - \mathbf { j } + \mathbf { k } )$
B) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( - \mathrm { i } + \mathbf { j } + \mathbf { k } )$
C) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } - \mathbf { j } - \mathbf { k } )$
D) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } - \mathbf { j } + \mathbf { k } )$
E) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } + \mathbf { j } + \mathbf { k } )$

Question

Find a unit vector orthogonal to u and v. $\begin{array} { l } 
\mathbf { u } = \mathbf { i } + \mathbf { j } \
\mathbf { v } = \mathbf { j } + \mathbf { k }
\end{array}$ 
A) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( - \mathbf { i } - \mathbf { j } + \mathbf { k } )$
B) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( - \mathrm { i } + \mathbf { j } + \mathbf { k } )$
C) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } - \mathbf { j } - \mathbf { k } )$ 
D) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } - \mathbf { j } + \mathbf { k } )$
E) $\text { Unit vector } = \frac { \sqrt { 3 } } { 3 } ( \mathbf { i } + \mathbf { j } + \mathbf { k } )$

Quizplus · Accepted Answer

The cross product of u and v is $\mathbf{i} - \mathbf{j} + \mathbf{k}$. The magnitude of this vector is $\sqrt{3}$, so the unit vector is $\frac{\sqrt{3}}{3}(\mathbf{i} - \mathbf{j} + \mathbf{k})$.

Find a Unit Vector Orthogonal to U and V u=i+jv=j+k\begin{array} { l } \mathbf { u } = \mathbf { i } + \mathbf { j } \\\mathbf { v } = \mathbf { j } + \mathbf { k }\end{array}u=i+jv=j+k​

Find a Unit Vector Orthogonal to U and V $\begin{array} { l } \mathbf { u } = \mathbf { i } + \mathbf { j } \\\mathbf { v } = \mathbf { j } + \mathbf { k }\end{array}$