Level:
Project ID:
1103212905
Accepted:
1
Clonable:
0
Easy:
0
A rectangle-based right pyramid \( ABCDV \) with its bottom edge length of \( 6 \) units and the perpendicular height of \( 6 \) units is placed in a coordinate system (see the picture). Find the parametric equations of an intersection line \( p \) of planes \( \alpha \) and \( \beta \), where \( \alpha \) passes through the points \( B \), \( C \) and \( V \), and \( \beta \) passes through the points \( A \), \( D \) and \( V \). What is the measure of an angle \( \varphi \) between the planes \( \alpha \) and \( \beta \). Round \( \varphi \) to the nearest minute.
\(\begin{aligned}
p\colon x&=3+t, & \varphi\doteq 53^{\circ}8'\\
y&=3, &\\
z&=6;\ t\in\mathbb{R} &
\end{aligned}\)
\(\begin{aligned}
p\colon x&=3+t, & \varphi\doteq 63^{\circ}8'\\
y&=3, &\\
z&=0;\ t\in\mathbb{R} &
\end{aligned}\)
\(\begin{aligned}
p\colon x&=3+t, & \varphi\doteq 53^{\circ}8'\\
y&=3+t, &\\
z&=6+2t;\ t\in\mathbb{R} &
\end{aligned}\)
\(\begin{aligned}
p\colon x&=3+t, & \varphi\doteq 63^{\circ}8'\\
y&=3, &\\
z&=6;\ t\in\mathbb{R} &
\end{aligned}\)