Give a vector parametric equation for the line (-4,-5,0) through the point that is parallel to the line

Question

Give a vector parametric equation for the line (-4,-5,0) through the point  that is parallel to the line  <2t-2, 3t-2, 5t-5):

turingtest · Answer

at which point are you stuck here?

anonymous · Answer

I understand the parametric equation, I had a question like it and I got it right, but I don't get how to find the line parallel to a parametric equation with only 1 point.

turingtest · Answer

what is the vector parallel to the line in this case? can you identify it?

anonymous · Answer

I'll try 1 sec

anonymous · Answer

The vector would be <2,3,5> would it be?

turingtest · Answer

yes

anonymous · Answer

and to be parallel it has to be a multiple of the values correct?

turingtest · Answer

right, plus a point on the line

turingtest · Answer

$$\vec r(t)=\vec P+\vec vt$$where $\vec v$ is the parallel vector and $\vec P$ is the position vector for a point on the line

anonymous · Answer

Yeah

anonymous · Answer

Ill try to work something out

anonymous · Answer

Wait so what am I trying to find right now? I am kind of confused. I found the vector [2,3,5] and the components (-2,-2,-5) and (0,1,0) and the point of the other line is -4,-5,0 and a vector parallel would be 4,6,10] [so I found a point that would make this right which would be 0,1,10 .... am I going about this right?

anonymous · Answer

Yes I got it right! Thanks

turingtest · Answer

welcome!
 (sorry I was afk there)