Problemas Resueltos - Razonamiento matemático
Problema 11
Si \( \vec{v} = (-2, \, 3) \) y \( \vec{w} = (3, \, -1) \), entonces \( -2 \vec{v} - (-3) \vec{w} \) es igual a :
-
\( (2, \, 3) \)
-
\( (-5, -9) \)
-
\( (5, \, 9) \)
-
\( (13, -6) \)
-
\( (13, -9) \)
Intenta resolverlo antes de ver la respuesta...
-
\( (13, -9) \)
En efecto:
\[
\begin{aligned}
&-2 \vec{v} – (-3) \vec{w}
\\[.5em]
&\hspace{1em}=
-2 ( -2, \, 3 ) – (-3) (3, -1)
\\[.5em]
&\hspace{1em}=
-2 (-2, \, 3) + 3(3, -1)
\\[.5em]
&\hspace{1em}=
( -2 (-2), -2 (3) ) + (3 (3), 3(-1))
\\[.5em]
&\hspace{1em}= (4, -6) + (9, -3)
\\[.5em]
&\hspace{1em}=
(4 + 9 , -6 -3)
\\[.5em]
&\hspace{1em}= \boldsymbol{ ( 13, -9 ) }
\end{aligned}
\]
\[
\begin{aligned}
-2 \vec{v} – (-3) \vec{w}
&=
-2 ( -2, \, 3 ) – (-3) (3, -1)
\\[.5em]
&=
-2 (-2, \, 3) + 3(3, -1)
\\[.5em]
&=
( -2 (-2), -2 (3) ) + (3 (3), 3(-1))
\\[.5em]
&= (4, -6) + (9, -3)
\\[.5em]
&=
(4 + 9 , -6 -3)
\\[.5em]
&= \boldsymbol{ ( 13, -9 ) }
\end{aligned}
\]