Do Vectors a, b, and c Satisfy the Right Hand Rule?

Click For Summary

Homework Help Overview

The discussion revolves around determining whether the vectors a=(1,2,3), b=(-1,2,-1), and c=(0,1,-2) satisfy the right-hand rule. Participants explore the relationships between these vectors, particularly through the concepts of cross products and dot products.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of the cross product of a and b equaling c to satisfy the right-hand rule. There are questions about how to determine if vectors are perpendicular and the implications of the dot product being zero. Some participants express confusion about the relevance of vector c in this context.

Discussion Status

The discussion is active with multiple interpretations being explored. Some participants suggest that linear independence of the vectors may be sufficient for satisfying the right-hand rule, while others focus on the calculations involving dot and cross products. There is no explicit consensus yet on the correct approach.

Contextual Notes

Participants are navigating the definitions and properties of vector operations, including the right-hand rule, without complete clarity on how these concepts interrelate in this specific case. The original poster expresses confusion regarding the requirements for the vectors to satisfy the right-hand rule.

Grawr
Messages
3
Reaction score
0
1. Homework Statement

Let a=(1,2,3) b=(-1,2,-1) and c=(0,1,-2). Do these vectors taken in this order, satisfy the right hand rule? Explain.


3. The Attempt at a Solution

I was told a cross b must equal c otherwise this is not satisfying? I'm VERY confused...can someone help out please and thanks?
 
Physics news on Phys.org
The cross product of a and b is perpendicular to both a and b.
how can you tell if two vectors are perpendicular?
 
Two vectors are perpendicular if the dot product is 0. So for example a cross b = c

So then a dot c should equal 0 and the same should go for b dot c. So if both do equal zero it must mean they do satisfy the rule correct?

EDIT: Ok nvm that does not help me out at all in my question.
 
Last edited:
Grawr said:
Two vectors are perpendicular if the dot product is 0. So for example a cross b = c

So then a dot c should equal 0 and the same should go for b dot c. So if both do equal zero it must mean they do satisfy the rule correct?

EDIT: Ok nvm that does not help me out at all in my question.

and if a dot c is not zero or b dot c is not zero, c cannot be the cross product of a and b.
 
Hmm so how does the c=(0,1,-2) play a role in here?
 
the fact that c=(0,1,-2) obviously plays a role in calculating the dot product of a and c or b and c.
 
You don't have to take cross products, all you need is that they are linearly independent and they are.

If you define the x-axis to point along a, y-axis to point along b and z-axis to point along c would your coordinate system be right handed? If so, then a-b-c in that order satisfies the right hand rule.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
2K
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
2K
  • · Replies 18 ·
Replies
18
Views
13K
  • · Replies 3 ·
Replies
3
Views
2K