Vectors b and c Parallel? Find Scalar s or N for No

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Homework Help Overview

The discussion revolves around determining whether two given vectors, b and c, are parallel. Participants are tasked with finding a scalar s such that c equals s times b, or indicating 'N' if they are not parallel. The vectors in question are b=<0,3,4>, c=<0,6,-8> for part a, and b=<10,6>, c=<-15,-9> for part b.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss their reasoning for determining the scalar s in relation to the vectors. There is an exploration of the conditions under which the vectors can be considered parallel, with specific calculations referenced.

Discussion Status

Some participants express confidence in their conclusions regarding the parallelism of the vectors and the corresponding scalar values. However, there is a call for further clarification on the reasoning behind selecting specific scalar values, indicating an ongoing exploration of the concepts involved.

Contextual Notes

Participants are encouraged to provide more detailed explanations for their choices, particularly regarding the scalar values used in their calculations. There is an emphasis on ensuring clarity in the reasoning process as part of the homework submission.

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Homework Statement


Given vectors b and c are they parallel? If so find such scalar s that c=sb, otherwise write N for no.

a) b=<0,3,4>, c=<0,6,-8)

b) b=<10,6>, c=<-15,-9>

Homework Equations



c=sb is a property of the dot product.

The Attempt at a Solution


For a) I put No because <0,6,-8> does not = <0s, 3s, 4s> because S=2
For b) I put Yes because S=-3/2 which would give you both outcomes of the vectors

Am I correct?
 
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Yes, you are. If you'd explain why you need to pick s=2 in the first case, that would probably help. "because s=2" isn't much of an explanation.
 
I put s=2 because I was finding a multiple of the two vectors given. Then I calculate 3s=6, that would then calculate to c=2.
 
tarheels88 said:
I put s=2 because I was finding a multiple of the two vectors given. Then I calculate 3s=6, that would then calculate to c=2.

Right, so the only possibility is s=2, and since that doesn't work there is no s that works. I knew you knew that. Just wanted you to add that if you are turning this in as a homework exercise.
 

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