Vector Equations for line passing through a point

[Peter G.]

Hi,

I am a bit confused... I don't understand what is happening, I can't picture it:

Find a vector equation for the line passing through the point 4,3 and parallel to the vector i - 2j.

If r = p +t (q-p)

I only have one point, how can I use the fact it is parallel to help me? Point Q must be as such that the dot product of q - p and i - 2j must equal the magnitude of q - p * the magnitude of i - 2j?

Any help is appreciated

Thanks,
Peter

 

[LCKurtz]

The vector equation of a line through (a,b) in the direction D = <c,d>is

<x,y> = <a,b> + t<c,d>

All you need is a point and a direction vector, which you have given.