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Tangent line to a curve in R3

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  • #1
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So the curve is defined as x-y^2 = 0, z= x . I'm supposed to find the tangent line to the curve. How do I find a slope in R3?
 

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  • #2
SammyS
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There are infinitely many such tangent lines.
 
  • #3
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Oh, right, I meant at the point (1,1,1).
 
  • #4
SammyS
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How do you write the "equation" of a line in R3?

Actually, how do you specify a line in R3?
 
  • #5
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something like (x1,y1,z1) + t(a,b,c)?
 
  • #6
Dick
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something like (x1,y1,z1) + t(a,b,c)?
Ok, can you write the curve (x,y,z) as a function of a single variable? Call that variable 't'.
 
  • #7
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Try letting t=x. Then, x=z=t, y=sqrt(t). So, a vector function for your curve should be r(t)= (t) i + (sqrt(t)) j + (t) k (let i, j, k be unit vectors).

Your point occurs at t=?

Find the slope of the vector function at that t, and plug into a vector equation for a line.
 

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