Rojas Romero
01/30/2023 · Elementary School
Equacions de rectes I Escriu les equacions vectorials i paramètriques de la recta que passa per \( A \) i té direcció paral•lela al vector \( \overrightarrow{\mathrm{d}} \) en cada cas: \( \begin{array}{ll}\text { a) } A(-3,7), \overrightarrow{\mathrm{d}}(4,-1) & \text { b) } A(-1,0), \overrightarrow{\mathrm{d}}(0,2) \\ \text { Obtén } 2 \text { punts més per a cada recta. }\end{array} \)
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### a) Punto \( A(-3, 7) \) y vector de dirección \( \overrightarrow{d}(4, -1) \)
- **Ecuación Vectorial:** \( \mathbf{r}(t) = (-3, 7) + t \cdot (4, -1) \)
- **Ecuaciones Paramétricas:**
\[
\begin{cases}
x = -3 + 4t \\
y = 7 - t
\end{cases}
\]
- **Puntos Adicionales:** \( B(1, 6) \) y \( C(5, 5) \)
### b) Punto \( A(-1, 0) \) y vector de dirección \( \overrightarrow{d}(0, 2) \)
- **Ecuación Vectorial:** \( \mathbf{r}(t) = (-1, 0) + t \cdot (0, 2) \)
- **Ecuaciones Paramétricas:**
\[
\begin{cases}
x = -1 \\
y = 2t
\end{cases}
\]
- **Puntos Adicionales:** \( B(-1, 2) \) y \( C(-1, 4) \)
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