Relative Position of Lines in Space

Submitted by vladimir.arzt on Thu, 05/23/2024 - 19:06
Project ID: 
7300000044
Accepted: 
SubArea: 
Space geometry
Type: 
Scrolling
Layout: 
8x8
Question: 
Let the x-axis, y-axis, and z-axis be the axes of a three-dimensional coordinate system. Let p denote a straight line. Match each given parametric expression of the line p with its correct position relative to the coordinate axes.
Questions Title: 
Parametric expression of the line p
Answers Title: 
Relative position of the line p to the coordinate axes
Question 1: 
x=2−2ty=−3z=4 } t∈R
Answer 1: 
The line p is parallel to the x-axis.
Question 2: 
x=2y=−3+3tz=4 } t∈R
Answer 2: 
The line p is parallel to the y-axis.
Question 3: 
x=2y=−3z=4−4t } t∈R
Answer 3: 
The line p is parallel to the z-axis.
Question 4: 
x=2−ty=−3+3tz=4−4t } t∈R
Answer 4: 
The line p intersects the x-axis only.
Question 5: 
x=2−2ty=−3+tz=4−4t } t∈R
Answer 5: 

The line p intersects the y-axis only.

Question 6: 
x=2−2ty=−3+3tz=4−t } t∈R
Answer 6: 
The line p intersects the z-axis only.
Question 7: 
x=2−2ty=−3+3tz=4−4t } t∈R
Answer 7: 
The line p intersects all coordinate axes.
Question 8: 
x=2−ty=−3+tz=4−t } t∈R
Answer 8: 
The line p is skew to all coordinate axes.