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this is parametric form of the line

parallel to omits the component its paralelling right?

same others, diff y then lol

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

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

m not getting u at all :(

well, the unit vector; tha thas the same direction but a magnitude of 1 would be:
<0,1,1>

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

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

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

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

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

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

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

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

i missed that 0 at the end :)

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

you see that?

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

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

its just a standard for notation really

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

as long as it aint a zero vecotr that is lol

yes :)

thank you so much to help me understand it :)

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