Equation of Line: (-1,2,-3) + t(1,-1,-1)

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Homework Help Overview

The discussion revolves around finding the equation of a line given a point and a direction vector. The original poster presents the point (-1, 2, -3) and the direction vector (1, -1, -1), expressing uncertainty about how to formulate the line's equation in this context.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to relate their understanding of lines defined by two points to the current problem involving a single point and a direction vector. They seek clarification on how to derive the line's equation from this information.

Discussion Status

Some participants offer suggestions, such as considering dot products and cross products, while others propose checking the derived equation against known methods for finding lines through two points. The conversation reflects a mix of exploration and validation of the original poster's thought process.

Contextual Notes

The original poster expresses a desire for guidance rather than a direct answer, indicating a focus on understanding the underlying concepts rather than simply obtaining a solution.

embury
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Homework Statement



I need to find the equation for the line that passes through the pont (-1, 2, -3) in the direction of the vector (1,-1,-1)

Homework Equations



The equation needs to be in the form v(t)=v subscript 0 + tv

The Attempt at a Solution


I know how to find the equation of a line passing through two points, but I have no idea how to find the equation with only one point heading in the direction of a vector. I'm not really looking for the answer, I'm looking for an explanation on how to find the equation of a line given one point in the direction of a vector. Any help would be appreciated. Thank you.

I think I've found the solution, but I'm not sure. v=(1,-1,-1) and V subscript 0 = (-1,2,-3), therefore the equation of the line is (-1,2,-3) + t(1,-1,-1). Is this right?
 
Last edited:
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Take a look at dot products and cross products.
 
I'm not sure if your answer is correct, but one way to check it is to use what you already know -- how to find the equation based on two points. Since the line is in the direction of (1,-1,-1) from point (-1,2,-3), then a 2nd point on the line would just be (1,-1,-1) away from the first point, right?
 
Thank you. I guess this question isn't that difficult. For some reason I thought it was harder than it was. :blushing: Thank you guys.
 
Actually, after the very good response to the "eigenvalue" question, yes, you should be embarrased!:smile:
 

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