Question

Find a vector parametric equation $$\vec{r}(t)$$ for the line through the points P=(−1,−4,2) and Q=(−1,1,−3) for the given conditions on the parameter t.

If $$\vec{r}(3)=P$$ and $$\vec{r}(6)=Q$$

Answer 1

I tried some guess and check but cant seem to get it

Answer 2

is there an algebraic way to do this im not getting?

Answer 3

r(3) = P

useually you get r(0) = P

so this is like you're shifting the line to right by 3 units

Answer 4

whats the transformation rule for shifting the graph of f(t) to right by 3 units ?

Answer 5

f(t) --> f(t-3)

yes ?

Answer 6

hmm im not aware of that rule

Answer 7

Okay, side question :
consider f(x) = x^2
whats the new equation after shifting above graph to right by 3 units ?

Answer 8

hmmm

Answer 9

i guess (x-3)^2?

Answer 10

see if you can go thru this quick
http://www.mathsisfun.com/sets/function-transformations.html

Answer 11

f(x) = (x-3)^2

Answer 12

Yes! easy, isnt it ?

Answer 13

yes, I learned that I think a long time ago and forgot

Answer 14

happens :) see if below satisfies the given conditions now :
\[\langle -1, -4, 2\rangle + \frac{t-3}{3}\langle 0, 5, -5\rangle \]

Answer 15

it does, but why divide by 3?

Answer 16

to slow down the speed by a factor of 3 because you want to take 3 units in going from P to Q :

r(3) = P
r(6) = Q

6-3 = 3

Answer 17

we wont be dividing by 3 if the conditions were like below :

r(3) = P
r(4) = Q

Answer 18

ahhh, interesting

Answer 19

tyvm :), I have a part 3 to this question which im not even sure what its asking..

Answer 20

If the points P and Q correspond to the parameter values t=0 and t=−4, respectively

Answer 21

i will post up a new question

Answer 22

I mean I think I understand each question by itself, but I would think it should help me do the next question, but I get stuck on every one of them

Answer 23

its okay, lets try and figure out here :)

Answer 24

I mean I understand each question after getting help

Answer 25

k

Answer 26

so I think it means that if i have r(0) it will give me P and if I have r(4) it will give me Q?

Answer 27

`If the points P and Q correspond to the parameter values t=0 and t=-4, respectively`

this is the question ?

Answer 28

yes, thats t = -4 sorry

Answer 29

so you want to reach point P at t=0
and reach point Q at t = -4

Answer 30

think of "t" as time if it helps..

Answer 31

clearly you're going back in time

Answer 32

try this :
\[\langle -1, -4, 2\rangle + \frac{-t}{4}\langle 0, 5, -5\rangle \]

Answer 33

yep that did work, wow, why cant i think of this :(

Answer 34

i did try t/4

Answer 35

you just need to see it worked one time, im sure you will figure it out by yourself next time :)

Answer 36

i hope so :), ty so much, really appreciate it

Answer 37

yw!