1103212206

SubArea:

Level:

Project ID:

1103212206

Accepted:

Clonable:

Easy:

A cube

A B C D E F G H

with an edge length of

2

is placed in a coordinate system (see the picture). Let

p

be a line of intersection of planes

α

and

β

, where

α

is passing through

C

F

and

H

and

β

is passing through

A

F

and

H

. Find the parametric equations of the line

p

and calculate the angle

φ

between planes

α

and

β

. Round

φ

to the nearest minute.

\begin{aligned} p : x & = t, & φ & ≐ 70^{\circ} 32^{'} \\ y & = t, \\ z & = 2; t \in R, \end{aligned}

\begin{aligned} p : x & = 2 t, & φ & ≐ 90^{\circ} \\ y & = 2 t, \\ z & = 2 + 2 t; t \in R, \end{aligned}

\begin{aligned} p : x & = t, & φ & ≐ 90^{\circ} \\ y & = t, \\ z & = 2; t \in R, \end{aligned}

\begin{aligned} p : x & = 2 t, & φ & ≐ 70^{\circ} 32^{'} \\ y & = 2 t, \\ z & = 2 t; t \in R, \end{aligned}

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