Vector Cross Product: Perpendicular Vectors lV_1 x V_2l

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Homework Help Overview

The discussion revolves around the properties of the vector cross product, particularly in the context of perpendicular vectors V_1 and V_2. Participants are exploring the implications of vector orientation and the mathematical definitions involved in calculating the cross product.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the conditions under which the cross product yields specific results, particularly focusing on the relationship between the angles of the vectors and the resulting magnitude of the cross product. There is also a discussion about the dimensional constraints of the cross product.

Discussion Status

The conversation is active, with participants engaging in clarifying the definitions and properties of the cross product. Some guidance has been offered regarding the relationship between the vectors and their angles, though there is no explicit consensus on the correct formulation yet.

Contextual Notes

There is a mention of dimensionality, indicating that the discussion is limited to three-dimensional space, which may affect the interpretation of the cross product. Additionally, a sign ambiguity in the magnitude calculation has been noted, suggesting further exploration is needed.

horsegirl09
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If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.
 
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horsegirl09 said:
If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.
The cross product is a vector perpendicular to V_1 and V_2. Also V_1 and V_2 don't have to be perpendicular to each other, only not parallel.

Note that this only makes sense in 3 dimensional space.

Further note: the magnitude is |V_1|x|V_2|cos(a), where a is the angle between the vectors. There is a sign ambiguity.
 
Last edited:
Isn't it |V_1|*|V_2|*sin(a)?
 
ehj said:
Isn't it |V_1|*|V_2|*sin(a)?

You're right - my bad.
 

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