Vectors

May 2010
3
0
Hi, I'm really confused and need some help

Consider the vectors u = (3,4) v= (7,0), w= (6, -2) with endpoints U, V and W respectively

c) Find the point P at which the directed line segment UW crosses vector v
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Hi, I'm really confused and need some help

Consider the vectors u = (3,4) v= (7,0), w= (6, -2) with endpoints U, V and W respectively

c) Find the point P at which the directed line segment UW crosses vector v
Strictly speaking a vector does not have an "endpoint" so I presume you are thinking of the representation as "arrows" with one end at the origin.

Then we can write vector v as the line segment from (0, 0) to (7, 0) (on the x-axis) which has parametric equations x= 7t, y= 0, with t going from 0 to 1.

Similarly, the "directed line segment" UW is the line from (3,4) to (6, -2) which has "direction vector" <6- 3, -2- 4>= <3, -6> and parametric equations x= 3s+ 3, y= -6s+ 4 with going from 0 to 1. Is there a pair of values for t and s which give the same (x, y)?