Question

Need Help Understanding Vectors and Parametric Equations

Are these parametric equations equal?
x=2t-1 and y=-2t+2

VS

x=-1-2t
y=2+2t

Answer 1

I had to figure out parametric and vector equations

The book and I have different answers, but I think thats allowed with parametric equations.

Answer 2

A(-1,2) and B(-3,4) are the two original points btw

Answer 3

to figure out AB i figured it doesnt amtter if I do A-B or B-A

Answer 4

a vector equations: given a direction vector <d> and an anchor point p

L = p + <d>t

Answer 5

vectors like to have positive first parts .... but yeah, it doesnt really matter overall

Answer 6

But when I graphics those two sets of equations seperately
They turned out to eb perpendicular to one another

Answer 7

a parameteric setup takes the point and vector apart:

x = px + dx*t
y = py + dy*t
z = pz + dz*t

etc ...

Answer 8

A(-1,2) and B(-3,4)
+1-2 +1-2
--------
-2,2 ; or vector (1,-1)

Answer 9

I'm just confused if I am getting some step wrong or if I am doing everything correctly, so I just have to check if

x=2t-1 and y=-2t+2

is the same as

x=-1-2t
y=2+2t

Answer 10

use either point, say p = (-1,2)

L1 = (-1,2) + (1,-1)t

x = -1+ t
y = 2 - t

Answer 11

The vector equation I got was (-1,2)+t(2,-2)
While the book got (-1,2)+t(-2,2)

Answer 12

Right I got that, but is my answer the same as the books in essence?

Answer 13

Am I technically correct?

Answer 14

Is (-1,2)+t(-2,2) the same as (-1,2)+t(-2,2)

Answer 15

is (-1,2)+t(-2,2)
the same as (-1,2)+t(-2,2)

typo ??? they are the same

Answer 16

no sorry
Is (-1,2)+t(-2,2) the same as (-1,2)+t(2,-2)

Answer 17

lol, they are the same, the vector the book gives is an exact result of A to B is all

Answer 18

the direction vector need not be the same length since for any real value t, it gets scaled to reach any point in the line

Answer 19

ok so it is correct regardless if it is 2,-2 or -2,2

Answer 20

correct since:

(2,-2) scaled by -1 gets us: (-2,2) they are the same "vector" as far as a line is concerned. If your book wants you to be more anal .... id suggest the books results

Answer 21

but a vector is directional right>?

Answer 22

no the book sint too anal

Answer 23

yes, but when defining a line its immaterial ....

Answer 24

OHHH

Answer 25

ok lol awesome. cuz my parametrics are all perpendicular and i was confused

Answer 26

I thought if its a vector it always eneds direction