Creating equations that meet certain conditions given 1 3D line

JohnySquid88

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Jun 19, 2024
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How would I go about solving a problem like this:
- I am given a line in 3D, vector form and I have to come up with an equation for a line for each of the following scenarios:

All these scenarios relate to Line 1 (L1) given in the question:
- A line that is collinear to L1
- A line that is coincident to L1
- A line that is skewed to L1
- A line that intersects with L1
 
 
The basic idea of lines in space let us derive three parametric equations. By them, we can describe any line in space.

What are these three equations?
 
How would I go about solving a problem like this:
- I am given a line in 3D, vector form and I have to come up with an equation for a line for each of the following scenarios:

All these scenarios relate to Line 1 (L1) given in the question:
- A line that is collinear to L1
- A line that is coincident to L1
- A line that is skewed to L1
- A line that intersects with L1
Can you give an example of the form in which you are "given" line L1, so we can be sure what you mean by "vector form"?

In what form are the four lines you are asked for meant to be expressed?

Have you looked up the meanings of collinear, coincident, skewed, and intersect? Have you considered how much freedom you have in choosing some of them (and how little you have for others)?

I'm wondering why you weren't also asked for concurrent lines or parallel lines.

In any case, we need to know something about what you are thinking, before we can know what help you need.
 
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