Ejemplos de multiplicación de vectores

1.-  u = {4 i; 3 j; -1 k}

v = {2 i; 6 j; 5 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 3
( 5) – 6(-1 ) i- ( 4 (5 ) -2 ( -1 ) ) j+ ( 4 ( 6 ) -2 ( 3) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
15+6) i- (20+2) j+ ( 24-6 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
21i-22j+18k\end{align}

2.- u = {4 i; 4 j; 7 k}

v = {-3 i; -1 j; -2 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 4
( -2) – (-1) 7 ) i- (4 ( -2 ) -(-3) 7 ) j+ ( 4 ( -1 ) -(-3) ( 4) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-8+7) i- (-8+21) j+ ( -4+12 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-1i-13j+8k\end{align}

3.- u = {1 i; 1 j; 5 k}

v = {5 i; 3 j; -2 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 1
( -2 ) – (3) 5 ) i- ( 1 ( -2 ) -5( 5 ) ) j+ ( 1 ( 3 ) -5 ( 1) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-2-15) i- ( -2-25) j+ ( 3-5 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-17i+27j-2k\end{align}

4.- u = {10 i; -3 j; 2 k}

v = {4 i; 5 j; 6 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( -3
( 6) – (5) 2 ) i- ( 10 (6 ) -4 ( 2 ) ) j+ ( 10 ( 5 ) -4 ( -3) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-18-10) i- ( 60-8) j+ ( 50+12 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-28i+52j+62k\end{align}

5.- u = {2 i; 3 j; 4 k}

v = {4 i;3 j; 2 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 3
( 2 ) – (3) 4) i- ( 2 (2 ) -4 ( 4 ) ) j+ ( 2 ( 3 ) -4 ( 3) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
6-12) i- ( 4-16) j+ ( 6-12 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-6i+12j-6k\end{align}

6.- u = {-5 i; -3 j; -8 k}

v = {-2 i; 6 j; 3 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 4
( -6 ) – (3) 5 ) i- ( 2 ( -6 ) -7 ( 3 ) ) j+ ( 2 ( 5 ) -7 ( 4) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-24-15) i- ( -12-21) j+ ( 10-28 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-39i+33j-18k\end{align}

7.- u = {3 i; 2 j; -4 k}

v = {6 i; 1 j; 3 k}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
u_{2} v_{3} -v_{2} u_{3} ) i- ( u_{1} v_{3} -v_{1} u_{3} ) j+ ( u_{1} v_{2}
-v_{1} u_{2} ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = ( 2
( 3 ) – 1 (-4) ) i- (3 ( 3 ) -6 ( -4 ) ) j+ ( 3 ( 1 ) -6 ( 2) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
6+4) i- (9+24) j+ ( 3-12 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
10i-33j-9k\end{align}