Solving a Dot Product Vector Problem (-1,0)

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Homework Help Overview

The problem involves finding two vectors, v1 and v2, that sum to (-1,0), with v1 being parallel to (5,-5) and v2 being perpendicular to (5,-5). The context is within vector mathematics, specifically focusing on vector addition and properties of parallel and perpendicular vectors.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss expressing v1 and v2 in terms of their components, with one suggesting that v1 can be represented as (k5, -k5) and v2 as being parallel to (5,5). Questions are raised about how the vector sum relates to the given target vector (-1,0) and what this implies for the components of v1 and v2.

Discussion Status

The discussion is ongoing, with some participants offering insights into the relationships between the vectors and their components. There is a request for further clarification on the dot product and its relevance to the problem, indicating a productive exploration of the concepts involved.

Contextual Notes

One participant expresses difficulty in following the directions and requests a solution, highlighting the challenge of the problem. There is also a mention of the dot product, suggesting that participants are considering various aspects of vector relationships.

ih8calc
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Hello, I have this problem that asks the following

Homework Statement


Find two vectors v1 and v2 whose sum is (-1,0) where v1 is parallel to (5,-5) while v2 is perpendicular to (5,-5).

Could someone "walk" me thought the steps to find v1 and v2... I'm confident I can make the computations is the steps that are unknown to me... thanks in advance...
 
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If v1 is parallel to (5,-5) then v1 = (k5,-k5). k is an unknown that you will need to solve for.

A similar setup applies to v2. v2 is perpendicular to (5,-5) so it is parallel to (5,5).
 
The first step would be to write the unknown vectors in terms of there unknown components: v_1=(x_1,y_1) and v_2=(x_2,y_2)...what is v_1+v_2 in terms of these components?...what does the fact that this vector sum must be (-1,0) tell you?
 
...okay, so maybe I can't follow directions as well as I thought... I hate to ask, but could you solve it for me? it's one of those things where I'm just stumped...
 
Why don't you show us what you've got? (even if you think it is wrong)
 
ih8calc said:
...okay, so maybe I can't follow directions as well as I thought... I hate to ask, but could you solve it for me? it's one of those things where I'm just stumped...
Since you titled this "dot product" why don't you tell us what you think the dot product is and how it is related to "perpendicular".
 

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