Finding the equation of a parametric curve

[rylz]

1. if y(t)= (a/t, b/t, c/t)



2. Prove that this curve is a straight line. Find the equation of the line



3. i found the first part without a problem, i just am not sure how to find the equation f the line.

 

[LCKurtz]

1. if y(t)= (a/t, b/t, c/t)



2. Prove that this curve is a straight line. Find the equation of the line



3. i found the first part without a problem, i just am not sure how to find the equation f the line.

Apparently $y(t)$ is a vector instead of the second component of the right side? How did you show it is a straight line without finding its equation? And what does "the equation f " mean? What forms do you know for straight line equations in 3D?

 

[rylz]

y(t) is the parametric curve, and i proved its a straight line by proving the curvature of the line. the "f" is supposed to be of

 

[Dick]

y(t) is the parametric curve, and i proved its a straight line by proving the curvature of the line. the "f" is supposed to be of

Proving the curvature is 0 is probably the hard way. Like LCKurtz said, "What forms do you know for straight line equations in 3D?"

 

[rylz]

x-x_o/a=y-y_o/b=z-z_o/c

 

[Dick]

x-x_o/a=y-y_o/b=z-z_o/c

That's a good one. It would be even better with pararentheses. Your parametric form is x=a/t, y=b/t, z=c/t. So?

 

[rylz]

so do i sub in a point for t in the domain? and that will give <x_o,y_o, z_o> and then how do i find the direction <a,b,c>.

 

[Dick]

so do i sub in a point for t in the domain? and that will give <x_o,y_o, z_o> and then how do i find the direction <a,b,c>.

Try subbing <x_o,y_o,z_o>=<0,0,0>.

 

[rylz]

and then the direction (a,b,c) would be point on the line or would it just be (a,b,c)?

 

[Dick]

and then the direction (a,b,c) would be point on the line or would it just be (a,b,c)?

Well, x/a=1/t, y/b=1/t, z/c=1/t. So x/a=y/b=z/c. Direction vector? Point on the line? Or BOTH?