# Equation of a line

## 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.

berkeman
Mentor
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. Thank you guys.

HallsofIvy
Actually, after the very good response to the "eigenvalue" question, yes, you should be embarrased! 