Question

Find an equation of the following lines.
The line through (0,0, 1) parallel to the y-axis.

I don't get why the answer is r(t)= <0, 0, 1> + t<0, 1, 0>

Answer 1

this is parametric form of the line

Answer 2

parallel to omits the component its paralelling right?

Answer 3

we can pick to point; or vectors that point to 2 points and create a line from them

P(x,y,z) = (0,0,1)

another point that is parallel to the y mean that the ys are the same right? for instance

(0,0,0) and (0,6,0) i guess i had that backewards lol

Answer 4

same others, diff y then lol

Answer 5

(0,0,1) and lets say (0,4,1) should be parallel to the y right?

Answer 6

it draws out right then :)

we need a vector from one point to the other now;

<0,4,1> works good right?

Answer 7

so do you mean that i can pick any point as long as y value stay the same and z value is 1?

Answer 8

m not getting u at all :(

Answer 9

well, the unit vector; tha thas the same direction but a magnitude of 1 would be:

<0,1,1>

Answer 10

nah; the x and z are the same; the y can be any value

Answer 11

P(0,0,1) and Q(0,1,1) are in line and parallel to the y axis

Answer 12

can the answer be r(t) = <0, 0, 1> + t<0, any y value here, 1>?

Answer 13

this is the view looking straight at the x axis; and y is to the left and right and z i up and down.

Answer 14

the only way a line can be parallel to the y axis is to have z and x remain constant between points

Answer 15

yes it can; but to make things simple; they use a "unit" vector

Answer 16

so its length is 1; and then any value fo y just makes it scalar

Answer 17

the line is a point plus a vector right?

r(t) = P(0,0,1) + t<0,1,1> where t is a scalar amount

Answer 18

i missed that 0 at the end :)

Answer 19

ahh i see it; the vector is saying tha tit doesnt change from x to z; just the y value lol

Answer 20

you see that?

Answer 21

<0,1,0> means that it never stears away from the original x and z values; it just heads down y

Answer 22

oh i see. I see it now. but where did they get the vector <0, 1, 0>?

Answer 23

any vector pointing in the same direction will work; so they simply choose what is called a "UNIT" vector. It has the same direction; but its length is equal to "1"

Answer 24

its just a standard for notation really

Answer 25

its the direction you want ; the length of the vector doesnt matter

Answer 26

as long as it aint a zero vecotr that is lol

Answer 27

just to make sure I totally understand this concept. So if i write
r(t) = <0,0,1 > + t<0, 4, 0>, i'm still correct right?

Answer 28

yes :)

Answer 29

thank you so much to help me understand it :)

Answer 30

thank you for letting me :) the more i help the more I learn myself lol