Question

select the term that describes the intersection or union. use uppercase letters to name the figure.

a. \\(\vec{fd} \cup p\\)

a. \\(\vec{fg} \cap \vec{fd}\\)

a. \\(r \cap p\\)

Explanation:

Analyze the first operation

Using the Geometric Set Operations and Intersection and Union knowledge points:
We evaluate the union of ray \( \vec{FD} \) and plane \( P \), denoted as \( \vec{FD} \cup P \).
Since the ray \( \vec{FD} \) lies entirely within plane \( P \), its union with the plane is the entire plane itself.
Thus, the resulting figure is plane \( P \).
The dropdown selection is "Plane" and the named figure is "P".

Analyze the second operation

Using the Geometric Set Operations and Intersection and Union knowledge points:
We evaluate the intersection of ray \( \vec{FG} \) and ray \( \vec{FD} \), denoted as \( \vec{FG} \cap \vec{FD} \).
Both rays share only their starting endpoint, which is point \( F \).
Thus, the intersection is point \( F \).
The dropdown selection is "Point" and the named figure is "F".

Analyze the third operation

Using the Geometric Set Operations and Intersection and Union knowledge points:
We evaluate the intersection of line \( r \) and plane \( P \), denoted as \( r \cap P \).
Line \( r \) passes vertically through plane \( P \), intersecting it at exactly one point, which is point \( F \).
Thus, the intersection is point \( F \).
The dropdown selection is "Point" and the named figure is "F".

Answer:

Question 1

• Term: Plane
• Name: P

Question 2

• Term: Point
• Name: F

Question 3

• Term: Point
• Name: F