- #1
dark_omen
- 9
- 0
Okay, so I have two vectors a = <-6, 9, -3> and b = <2, -3, 1>. How can I test to see if these two vectors are parallel or not?
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How to find if a vector is parallel to another
In summary, to test if two vectors are parallel, we can check if there exists a real number c such that a=cb. Another approach is to use the definition of the cross product. Additionally, we can use the formula axb=det \left(\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k}\\a_{1} & a_{2} & a_{3}\\b_{1} & b_{2} & b_{3}\end{array}\right) for a=cb.
- #2
radou
Homework Helper
- 3,149
- 8
Vectors a and b are parallel if there exists a real number c such that a=cb. In your case it is pretty obvious.
- #3
dark_omen
- 9
- 0
What if it is not so obvious like the one I presented. Is there another approach to it (cross product of dot product ??)
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- #4
radou
Homework Helper
- 3,149
- 8
Think about the definition of the cross product, and see what happens. 
Btw, just use axb=[tex]det \left(\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k}\\a_{1} & a_{2} & a_{3}\\b_{1} & b_{2} & b_{3}\end{array}\right)[/tex] for a=cb.
Btw, just use axb=[tex]det \left(\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k}\\a_{1} & a_{2} & a_{3}\\b_{1} & b_{2} & b_{3}\end{array}\right)[/tex] for a=cb.1. How do I determine if two vectors are parallel?
To determine if two vectors are parallel, you need to calculate the cross product of the two vectors. If the cross product is equal to zero, then the vectors are parallel. If the cross product is not equal to zero, then the vectors are not parallel.
2. What is the formula for finding the cross product of two vectors?
The formula for finding the cross product of two vectors is:
(a,b,c) x (d,e,f) = (bf-ce, cd-af, ae-bd)
3. Can two non-zero vectors be parallel?
No, two non-zero vectors cannot be parallel. For two vectors to be parallel, they must have the same direction or be in the same line. If two vectors have different directions, they cannot be parallel.
4. How can I use dot product to determine if two vectors are parallel?
To use dot product to determine if two vectors are parallel, calculate the dot product of the two vectors. If the dot product is equal to the product of the magnitudes of the two vectors, then the vectors are parallel. If the dot product is not equal to the product of the magnitudes of the two vectors, then the vectors are not parallel.
5. Can two vectors be parallel if they are in different dimensions?
No, two vectors cannot be parallel if they are in different dimensions. In order for two vectors to be parallel, they must be in the same dimension (2D, 3D, etc.) and have the same direction or be in the same line.
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