How to approach solving for parallel vectors?

[pavadrin]

Hi
I’m given a series of problems in which I need to find the vector equation of a line which pass through a given point and are parallel to another vector.
The first problem:
Find a parallel vector to b = 5i-j, and passes through the point with position vector a = 2i+3j
My working:
r = a + λb
= (2i+3j) + λ(5i-j)
= (2+5λ)i + (3-λ)j
From this point onwards I do not have the slightest clue on where to go next, or if what I have done is correct. Could somebody please tell me if what I am doing is correct or incorrect, and if so, the correct way to approach these pesky problems.
Thanks
Pavadrin

 

[danago]

Looks fine to me so far, unless you need to write it as parametic or cartesian equations

From this point onwards I do not have the slightest clue on where to go next, or if what I have done is correct. Could somebody please tell me if what I am doing is correct or incorrect, and if so, the correct way to approach these pesky problems.
Thanks

Well that depends on what the question asks If it just asks for the vector equation of the line, then that's it.

Hi Nikki :D