- #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?
Thanks
Thanks
How to find if a vector is parallel to another
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SUMMARY
To determine if two vectors, specifically a = <-6, 9, -3> and b = <2, -3, 1>, are parallel, one must check if there exists a scalar c such that a = cb. The discussion emphasizes using the cross product method, defined as a x b = 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). If the result of the cross product is the zero vector, the vectors are parallel.
PREREQUISITES- Understanding of vector notation and operations
- Knowledge of scalar multiplication in vector mathematics
- Familiarity with the concept of the cross product
- Basic understanding of determinants in linear algebra
- Study the properties of the cross product in vector algebra
- Learn how to compute determinants for 3x3 matrices
- Explore the geometric interpretation of parallel vectors
- Investigate the relationship between dot product and vector angles
Students and professionals in mathematics, physics, and engineering who need to understand vector relationships and operations, particularly in the context of parallelism.
- #2
radou
Homework Helper
- 3,148
- 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 ??)
Thanks
Thanks
- #4
radou
Homework Helper
- 3,148
- 8
Think about the definition of the cross product, and see what happens. 
Btw, just use 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.
Btw, just use 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.Similar threads
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