Finding a vector perpendicular to a plane

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Homework Help Overview

The discussion revolves around finding a vector that is perpendicular to a plane defined by two vectors. Participants are exploring the properties of vector cross products and their implications in determining perpendicularity.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants question the choice of vector pairs for cross products, specifically why PQ cross PR is preferred over PR cross PQ, and why RP cross RQ was not chosen. There is also a discussion about the general property that any two non-parallel vectors in the plane can yield a perpendicular vector through their cross product.

Discussion Status

The conversation is active, with participants raising questions about vector operations and their order. Some guidance is provided regarding the properties of cross products, but there is no explicit consensus on the best approach to the problem.

Contextual Notes

Participants are considering the implications of vector orientation and the associative property of cross products, with some uncertainty about the order of operations in multiple vector cross products.

Miike012
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How did they know to do PQ cross PR instead of PR cross PQ?
And why did they not choose RP cross RQ?

Look at picture.
 

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Miike012 said:
How did they know to do PQ cross PR instead of PR cross PQ?
Since any vector that is perpendicular to the plane will do, it doesn't matter if they calculate PQ X PR or PR X PQ, which will just point the opposite direction.
Miike012 said:
And why did they not choose RP cross RQ?

Look at picture.

If you cross any two vectors in the plane that aren't parallel, you'll get a third vector that is perpendicular to the first two.
 
Another question:
if I have 3 vectors u,v, and w
If i am trying to find u cross v cross w do i cross u with v first then w or v cross w then u?
 
I'm pretty sure they associate left-to-right, so u X v X w would be the same as (u X v) X w.
 

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