Ejercicios de multiplicación de vectores 2 parte

Ejercicios de multiplicación de vectores 2 parte

En estos ejercicios se tienen los vectores u = {u₁, u₂, u₃} y v = {v₁, v₂, v₃} y se sustituyen en la formula para obtener W = U x V.

1.-  u = {2i; -3 j; 1 k}

v = {-5 i; -1 j; 4 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
(4) – (-1)(1) i- (2(4 ) -(-5) ( 1) ) j+ (2 (-1) -(-5) ( -3 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-12+1) i- (8+5) j+ ( -2-15 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-11i-13j-17k\end{align}

2.- u = {3 i; -2 j; -6 k}

v = {5 i; 7 j; 4 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)
( 4) – 7(-6) ) i- (3 ( 4 ) -(-6) 5) j+ ( 3 ( 7) -(5) (-2) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-8+42) i- (12+30) j+ ( 21+10) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
34i-42j+31k\end{align}

3.- u = {8 i; 1 j; -2 k}

v = {-3 i; 1 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} = (1
( 6) – 1 (-2) ) i- ( 8(6 ) -(-3)( -2 ) ) j+ ( 8( 1 ) -(-3) 1 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
6+2) i- ( 48-6) j+ ( 8+3 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
8i-42j+11k\end{align}

4.- u = {-2 i; 7 j; 5 k}

v = {3 i; -6 j; 7 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} = ( 7
( 7) – (-6)5 ) i- ( -2 (7 ) -3 ( 5 ) ) j+ ( -2 ( -6 ) -3 ( 7) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
49+30) i- ( -14-15) j+ ( 12-21 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
79i+29j-9k\end{align}

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

v = {1 i; 2 j; 4 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
(4 ) – 2 (-5)) i- ( 5 (4 ) – 1( -5 ) ) j+ ( 5 ( 2 ) -1 (-3) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
-12+10) i- (20+5) j+ (10+3 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
-2i-25j+13k\end{align}

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

v = {4 i; 9 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} = (-1
(-3 ) – 9(-1) ) i- ( 3 (-3 ) -4 ( -1 ) ) j+ ( 3 ( 9 ) -4 ( -1) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
3+9) i- ( -9+4) j+ ( 27+4 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
12i+5j+31k\end{align}

7.- u = {5 i; 10j; 4 k}

v = {8 i; 5 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} = (10
(3 ) – (5) (4) ) i- (5 (3) -8(4 ) ) j+ ( 5 (5 ) -8 ( 10) ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} = (
30-20) i- (15-32) j+ ( 25-80 ) k\end{align}

\begin{align}\overset{}{} \overset{\rightarrow}{u} \times \overset{\rightarrow}{v} =
10i+17j-55k\end{align}

Espero que estos ejercicios te hayan servido para practicar y ahora domines el tema, nos vemos… hasta la próxima!!