Parallel Vectors: Solving for a

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Homework Help Overview

The discussion revolves around determining the value of 'a' for which the vectors u=<2,4,-5> and v=<-4,-8,a> are parallel. The problem involves concepts from vector mathematics, specifically the conditions under which two vectors are parallel.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the cross product to find conditions for parallelism, with one participant expressing uncertainty about the next steps after calculating the cross product. Others suggest alternative methods, such as expressing one vector as a scalar multiple of the other.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some have pointed out potential errors in the initial calculations, while others have proposed a more straightforward method to determine parallelism.

Contextual Notes

There is a note that the original problem statement was incomplete, which may affect the clarity of the discussion. Additionally, participants are questioning the correctness of the components involved in the cross product calculation.

MozAngeles
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Homework Statement



for what value of a will the vectors u=<2,4,-5> and v=<-4,-8,a>

Homework Equations



(uXv)=0

The Attempt at a Solution


i took the cross product and got 4(a-10)i-2(a-10)j-32k=0

i don't know wher eto go from there do i set a-10=0 solve for a so my answer is ten?
 
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You didn't finish writing the problem statement.
 
Assuming you're trying to find which values of a make the two vectors parralell...

the k-hat component isn't right in what you've posted, and once you get that it's pretty straightforward to find the values of a so that's you get the zero vector as the cross product.
 
Hi MozAngeles! :smile:

There is an easier way to find 2 parallel vectors.
If u and v are parallel, one must be a multiple of the other.

That is, if you try to solve:

u = λv

that should have a single solution for λ and a.
 

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