How to Find the Tangent Line to a Curve in R3 Using Vector Functions?

[autre]

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?

 

[SammyS]

There are infinitely many such tangent lines.

 

[autre]

Oh, right, I meant at the point (1,1,1).

 

[SammyS]

How do you write the "equation" of a line in R³?

Actually, how do you specify a line in R³?

 

[autre]

something like (x1,y1,z1) + t(a,b,c)?

 

[Dick]

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'.

 

[schaefera]

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.