Vectors and Parametric Equations

[Cudi1]

Homework Statement

write the vector equation and parametric equation of the line through A(-1,2,1) and B(1,2,1)

Basically I was wondering If i found AB or BA would it be equivalent?

Homework Equations

AB= OB-OA= (1,2,1)-(-1,2,1) = (2,0,0)
BA= OA-OB= (-1,2,1)- (1,2,1) = (-2,0,0)

thus , (x,y,z)= (-1,2,1)+ t(2,0,0)
x=-1+2t
y=2
z=1

The Attempt at a Solution

I solved it at the top but found that AB=-BA, is that correct, and if i wanted to find b/w 2 points would AB=-BA ( as the questions I've dealt with this seems true?)

 

[LCKurtz]

Both parameterizations are correct. Once you have any point P on the line and any direction vector D then <x,y,z> = P + tD is a parameterization. So you could start at either point on the line and take any multiple of your direction vector and that would be correct. The only difference between the parameterizations is where they start and for which value of t there are "where".

 

[Cudi1]

okay, i think i get it so the only difference is that it is a scalar mutilple of -1?
thanks for the help

 

[HallsofIvy]

If you think of the parameter t as "time" you can think of moving along the line. Using AB rather than BA changes the direction in which you are moving but you are still on the same line. Also, you have a choice of using the coordinates of A or B in your formula (you have x= -1+ 2t, y= 2, z= 1 so you chose to use A= (-1, 2, 1)). That choice determines only where you "start" but still gives the same line.