mmm cool thanks, it just seems weird seeing as in the question they have OA = 500i+450j which is just a 'point', and yet they ask whether the vector function crosses the 'path' of OA. Wouldn't normally call a point a path rite?
LOL I remember that dodgy plane question!
(wait didn't they say the plane landed at (500,450) or something? soz memory is a bit weary here lol)
Here's the question
Relative to a fixed origin, O, the position of the plane, P, at time
is given by
 = (15t^2+30t)i+(10t^2-20t)j)
. An airport officilal is standing at A(500,450) and observes the plane landing, worried that he may be hit by the plane. State, giving reasons, whether the plane's path crosses the path of vector OA.
For two vector functions )
and )
Cross: for some arbitrary 
and 
,  = r_2(t_2))
(i.e. they cross the same point)
Collide: for some ,  = r_2(t_1))
(i.e. they cross the same point at the same time)
A path defined by the tip of the position vector described by r(t). Hence, when two paths cross, we're saying that the tips of two position vectors coincide. Since all position vectors originate from O, thus the two position vectors must coincide exactly for a 'cross'. For a collision, the two position vectors must coincide exactly at the time.
cool thanks mao! hate those tricky linguistics
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