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

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To find the equation of a line passing through the point (-1, 2, -3) in the direction of the vector (1, -1, -1), the correct form is v(t) = v₀ + tv, where v₀ is the point and v is the direction vector. The resulting equation is (-1, 2, -3) + t(1, -1, -1). The discussion emphasizes understanding the relationship between a point and a direction vector rather than relying solely on two points. Additionally, checking the solution by finding a second point along the line is suggested. The participants express that the problem is simpler than initially perceived.
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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?
 
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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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