- #1
r_swayze
- 66
- 0
How do I find the vector parallel to the line x+2 = 1/2y = z-3 ?
the book says its < 1,2,1 > but I have no idea how to get there?
the book says its < 1,2,1 > but I have no idea how to get there?
How to find a vector parallel to a line?
In summary, a vector parallel to a line has the same direction as the line and will never intersect with the line. To determine if a vector is parallel to a line, you can use the cross product or dot product. A vector can be parallel to multiple lines if those lines have the same direction. To find a vector parallel to a specific line, you can use the slope of the line. However, you cannot find a vector parallel to a line using only one point on the line.
- #2
tiny-tim
Science Advisor
Homework Helper
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Hi r_swayze! 
Just go for the obvious …
that line is parallel to the line x = 1/2y = z, from which it's pretty obvious that if you increase x by 1, the you increase y by 2, and z by 1
Just go for the obvious …
that line is parallel to the line x = 1/2y = z, from which it's pretty obvious that if you increase x by 1, the you increase y by 2, and z by 1
- #3
r_swayze
- 66
- 0
oh I think I see now, so the +2 and -3 from the x and z equations are just telling the shift in position?
- #4
tiny-tim
Science Advisor
Homework Helper
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Yup!
1. What is a vector parallel to a line?
A vector parallel to a line is a vector that has the same direction as the line. This means that the vector and the line will never intersect and will always remain the same distance apart.
2. How do I know if a vector is parallel to a line?
To determine if a vector is parallel to a line, you can use the cross product or dot product. If the cross product is equal to 0, then the vector is parallel to the line. If the dot product is equal to 0, then the vector is perpendicular to the line.
3. Can a vector be parallel to multiple lines?
Yes, a vector can be parallel to multiple lines if those lines have the same direction. In other words, if the lines are parallel to each other, then any vector parallel to one of the lines will also be parallel to the other lines.
4. How do I find a vector parallel to a specific line?
To find a vector parallel to a specific line, you can use the slope of the line. The slope of the line will give you the direction of the line, and you can use this to create a vector with the same direction as the line.
5. Can I find a vector parallel to a line using only one point on the line?
No, you cannot find a vector parallel to a line using only one point on the line. You need at least two points on the line to determine the direction of the line and therefore, the vector parallel to it.
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