3D geometry: parametric equation and tangents

  • #1
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I have a doubt in 3d geometry. I calculus and I know how to do partial derivatives.(but I don't know what it means).
If you have a parametric equation ##x=t, y=t^2,z=t^3## (the equation is randomn)
What does ##\vec{r}=t\hat{i}+t^2\hat{j}+t^3\hat{k}## represent?
now if it represents the position vector or the vector connecting origin and a point on the curve, then will ##\frac{dr}{dt}## give the tangent to the curve?
 
  • #2
I have a doubt in 3d geometry. I calculus and I know how to do partial derivatives.(but I don't know what it means).
If you have a parametric equation ##x=t, y=t^2,z=t^3## (the equation is randomn)
What does ##\vec{r}=t\hat{i}+t^2\hat{j}+t^3\hat{k}## represent?
It represents a curve in three-dimensional space. For each value of the parameter t, you get a vector from the origin to a point on the curve. To see what this curve looks like, plot 8 or 10 points and connect them.
AdityaDev said:
now if it represents the position vector or the vector connecting origin and a point on the curve, then will ##\frac{dr}{dt}## give the tangent to the curve?
Yes
 
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