# Thread: Linear Algebra Lines vs. Vectors

1. ## Linear Algebra Lines vs. Vectors

Hi, I'm new to the forum, and to linear algebra. Not having much fun with that latter, I'm afraid. So I hope that this helps me understand the concepts that it deals with.
I guess I'll start with a question, try to work my way through it, and hopefully get it right, but if not, please correct me, and tell me where I went wrong and why.

Find the equation of the line parallel to v=(5,-2,1) passing through the point (1,6,2), and determine whether the point (5,4,3) is on this line.

I think that the equation of the line would be x=(1,6,2) + t (5,-2,1), because this would mean that (1,6,2) is on the line, and that the line has a direction of (5,-2,1). I'm not exactly sure how to figure out if the point is on the line, or if I'm even going in the right direction with this problem...

2. Originally Posted by Hellreaver
Find the equation of the line parallel to v=(5,-2,1) passing through the point (1,6,2), and determine whether the point (5,4,3) is on this line.
I think that the equation of the line would be x=(1,6,2) + t (5,-2,1)
You are correct!
Now, is there a value of t for which x=(5,4,3)?

3. So would it then become:

(5,4,3)= (1,6,2) + t (5,-2,1)
(5,4,3)-(1,6,2)=t (5,-2,1)
(4,-2,1)= t (5,-2,1)

and since the x values are different, and changing t from 1 to any other number would change the values of y and z, the point is not on the line?

Edit: Wow, dumb question, of course it isn't. Alright, thanks a bunch for that. I have another one, kinda similar to the first, but I'm not sure how to go about it...

Find parametric equations of the line that is perpendicular to the plane x+2y+3z=4 and passes through the point (1,1,-1).

I'm not even sure where to being on this one... Should I solve for x in the equation of the plane, or what?