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

[Grawr]

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?

 

[kamerling]

The cross product of a and b is perpendicular to both a and b.
how can you tell if two vectors are perpendicular?

 

[Grawr]

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.

 

[kamerling]

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.

 

[Grawr]

Hmm so how does the c=(0,1,-2) play a role in here?

 

[kamerling]

the fact that c=(0,1,-2) obviously plays a role in calculating the dot product of a and c or b and c.

 

[DavidWhitbeck]

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.