Question

the intersection of plane r and plane p is
.
point
is not on plane p.
$overleftrightarrow{ce}$ and $overleftrightarrow{db}$ intersect at point
.

Explanation:

First Blank (Intersection of Plane R and Plane P):

Step1: Recall Plane Intersection Rule

Two planes intersect in a line. From the diagram, plane R (vertical) and plane P (horizontal) intersect along the line containing points like B, D, etc. Looking at the line segments, the intersection line is the line through B, D, and the common edge. The line here is \(\overleftrightarrow{BD}\) (or the line with points B, D, and the line of intersection). But from the points, the intersection is the line containing B, D, and the line where the two planes meet. So the intersection is a line, specifically the line through B and D (or the line with points like B, D, C, E? Wait, no, plane R is vertical, plane P is horizontal. Their intersection is the line where they cross, which is the line with points B, D, and the line segment CE? Wait, no, looking at the diagram, plane R has points F, G, B, D; plane P has points C, D, B, E, H? No, H is outside. Wait, the intersection of two planes is a line. So the line here is \(\overleftrightarrow{BD}\) (or the line containing B and D, and the line where the two planes meet). So the intersection is the line, say, \(\overleftrightarrow{BD}\) (or the line with points B, D, and the line of intersection). But from the diagram, the common line is the line through B and D (and the line segment CE? Wait, no, CE is on plane P, and BD is on both? Wait, plane R (vertical) and plane P (horizontal) intersect along the line that has points B, D, and the line where they cross. So the intersection is a line, so the answer is the line, e.g., \(\overleftrightarrow{BD}\) (or the line with points B, D, and the line of intersection). But looking at the points, the intersection is the line containing B and D (and the line segment CE? No, CE is on plane P, BD is on both. So the intersection is the line \(\overleftrightarrow{BD}\) (or the line through B and D, which is the edge of both planes).

Step2: Identify the Line

From the diagram, plane R (vertical) and plane P (horizontal) intersect along the line that includes points B, D, and the line where they cross. So the intersection is the line, for example, \(\overleftrightarrow{BD}\) (or the line with points B, D, and the line of intersection). So the first blank is the line, say, \(\overleftrightarrow{BD}\) (or the line through B and D, which is the common line of the two planes).

Second Blank (Point not on Plane P):

Step1: Recall Plane Definition

A plane contains all points on it. Plane P is the horizontal plane. Points F, G, H, L are outside? Wait, plane P has points C, D, B, E. Points F is on plane R (vertical), G is on plane R, H is above, L is below. So points not on plane P: F, G, H, L. Let's check: Plane P is the horizontal one. Point F is on plane R (vertical), so not on P. Point G is on plane R, not on P. Point H is above, not on P. Point L is below, not on P. But from the diagram, F is on plane R (vertical), so not on P. So possible points: F, G, H, L. Let's see the options. The point F is on plane R, so not on P. So the second blank is F (or G, H, L; but F is on plane R, so likely F).

Third Blank (Intersection of \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{DB}\)):

Step1: Recall Line Intersection Rule

Two lines intersect at a point. \(\overleftrightarrow{CE}\) is the horizontal line on plane P, \(\overleftrightarrow{DB}\) is the vertical line (or the line through D and B) on both planes. They intersect at point D (or B? Wait, looking at the diagram, \(\overleftrightarrow{CE}\) goes through C, D, E; \(\overleftrightarrow{DB}\) goes through D, B. So their intersection is point D. Wait, no: \(\overleftrightarrow{CE}\) is C---D---E, \(\overleftrightarrow{DB}\) is D---B. So they intersect at D.

Answer:

s:

1. The intersection of plane R and plane P is \(\boldsymbol{\overleftrightarrow{BD}}\) (or the line containing B and D, e.g., \(\overleftrightarrow{BD}\)).
2. Point \(\boldsymbol{F}\) (or G, H, L; F is a common choice) is not on plane P.
3. \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{DB}\) intersect at point \(\boldsymbol{D}\).

(Note: Depending on the diagram's exact labeling, the first line could be \(\overleftrightarrow{BD}\) or \(\overleftrightarrow{CE}\)? Wait, no, plane R is vertical, plane P is horizontal. Their intersection is the line where they cross, which is the line that is the edge of both. So if plane R is vertical (like a wall) and plane P is horizontal (like a floor), their intersection is a vertical line? No, wait, in the diagram, plane R is vertical (the upright plane) and plane P is horizontal (the flat plane). Their intersection is the line where they meet, which is the line containing B, D, and the line segment that is the common edge. So \(\overleftrightarrow{BD}\) is that line. For the second point, F is on plane R, so not on P. For the third, \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{DB}\) intersect at D, since \(\overleftrightarrow{CE}\) passes through D and \(\overleftrightarrow{DB}\) passes through D.)