Level:
Project ID:
1103212206
Accepted:
1
Clonable:
0
Easy:
0
A cube \( ABCDEFGH \) with an edge length of \( 2 \) is placed in a coordinate system (see the picture). Let \( p \) be a line of intersection of planes \( \alpha \) and \( \beta \), where \( \alpha \) is passing through \( C \), \( F \) and \( H \) and \( \beta \) is passing through \( A \), \( F \) and \( H \). Find the parametric equations of the line \( p \) and calculate the angle \( \varphi \) between planes \( \alpha \) and \( \beta \) . Round \( \varphi \) to the nearest minute.
\( \begin{aligned}
p\colon x&=t, & \varphi&\doteq 70^{\circ}32' \\
y&=t, & &\\
z&=2;\ t\in\mathbb{R}, & &
\end{aligned} \)
\( \begin{aligned}
p\colon x&=2t, & \varphi&\doteq 90^{\circ} \\
y&=2t, & & \\
z&=2+2t;\ t\in\mathbb{R}, & &
\end{aligned} \)
\( \begin{aligned}
p\colon x&=t, & \varphi&\doteq 90^{\circ}\\
y&=t, & & \\
z&=2;\ t\in\mathbb{R}, & &
\end{aligned} \)
\( \begin{aligned}
p\colon x&=2t, & \varphi&\doteq 70^{\circ}32' \\
y&=2t, & & \\
z&=2t;\ t\in\mathbb{R}, & &
\end{aligned} \)