Finding a Vector Perpendicular to One Vector and Parallel to Another

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Homework Help Overview

The discussion revolves around finding a vector \( u \) that is both perpendicular to a given vector \( v \) and parallel to a plane defined by a normal vector \( n \). The problem involves concepts from vector mathematics, specifically the relationships between dot and cross products.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationships between the vectors using dot and cross products. The original poster notes that \( u \) must satisfy conditions related to both \( v \) and \( n \). Some participants suggest considering the cross product as a potential method to find \( u \).

Discussion Status

There is an ongoing exploration of the relationships between the vectors, with hints being provided regarding the use of the cross product. Some participants affirm the idea that \( u \) could be expressed as the cross product of \( n \) and \( v \), while also noting that any multiple of this vector would satisfy the conditions.

Contextual Notes

Participants are working within the constraints of a homework problem, which limits the provision of complete solutions. There is an emphasis on understanding the underlying vector relationships rather than simply arriving at an answer.

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Homework Statement



Suppose n is normal to a plane and v is parallel to the plane. Describe how you would find a vector u that is both perpendicular to v and parallel to the plane.



Homework Equations



Cross product, dot product

The Attempt at a Solution



Since u is perpendicular to v, u dot v = 0. U is also parallel to the plane so u will be perpendicular to n, so u dot n=0.

How would I do the rest of it ?
 
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Well, I can't give you the solution, but I will tell you that if I gave you a hint, you'd probably know it. Let's try.

You've used the dot product. Does the cross product help?
 
You didn't use the cross product. axb is perpendicular to both a and b, right?
 
Oh so u is basically n cross v ?
 
nns91 said:
Oh so u is basically n cross v ?

Sure. Or any multiple thereof.
 

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