anonymous
  • anonymous
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>
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
this is parametric form of the line
amistre64
  • amistre64
parallel to omits the component its paralelling right?
amistre64
  • amistre64
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

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amistre64
  • amistre64
same others, diff y then lol
amistre64
  • amistre64
(0,0,1) and lets say (0,4,1) should be parallel to the y right?
amistre64
  • amistre64
it draws out right then :) we need a vector from one point to the other now; <0,4,1> works good right?
anonymous
  • anonymous
so do you mean that i can pick any point as long as y value stay the same and z value is 1?
anonymous
  • anonymous
m not getting u at all :(
amistre64
  • amistre64
well, the unit vector; tha thas the same direction but a magnitude of 1 would be: <0,1,1>
amistre64
  • amistre64
nah; the x and z are the same; the y can be any value
amistre64
  • amistre64
P(0,0,1) and Q(0,1,1) are in line and parallel to the y axis
amistre64
  • amistre64
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anonymous
  • anonymous
can the answer be r(t) = <0, 0, 1> + t<0, any y value here, 1>?
amistre64
  • amistre64
this is the view looking straight at the x axis; and y is to the left and right and z i up and down.
amistre64
  • amistre64
the only way a line can be parallel to the y axis is to have z and x remain constant between points
amistre64
  • amistre64
yes it can; but to make things simple; they use a "unit" vector
amistre64
  • amistre64
so its length is 1; and then any value fo y just makes it scalar
amistre64
  • amistre64
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
amistre64
  • amistre64
i missed that 0 at the end :)
amistre64
  • amistre64
ahh i see it; the vector is saying tha tit doesnt change from x to z; just the y value lol
amistre64
  • amistre64
you see that?
amistre64
  • amistre64
<0,1,0> means that it never stears away from the original x and z values; it just heads down y
anonymous
  • anonymous
oh i see. I see it now. but where did they get the vector <0, 1, 0>?
amistre64
  • amistre64
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"
amistre64
  • amistre64
its just a standard for notation really
amistre64
  • amistre64
its the direction you want ; the length of the vector doesnt matter
amistre64
  • amistre64
as long as it aint a zero vecotr that is lol
anonymous
  • anonymous
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?
amistre64
  • amistre64
yes :)
anonymous
  • anonymous
thank you so much to help me understand it :)
amistre64
  • amistre64
thank you for letting me :) the more i help the more I learn myself lol

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