13.1 Vector Functions and Space Curves (Examples)

Example (i)

ParametricPlot3D[{Sin[t],Cos[t],Sqrt[t]},{t,0,6Pi},AxesLabel->{x,y,z},AspectRatio->1]

Example (ii)

ParametricPlot3D[{t,(t^2),(t^3)-t},{t,-2,2},AxesLabel->{x,y,z},AspectRatio->1]

Example (iv)

p1=ContourPlot3D[{((y^2)/4)+((z^2)/16)==1,x+2y+3z==6},{x,-10,20},{y,-5,5},{z,-5,5},AxesLabel->Automatic];
p2=ParametricPlot3D[{6-4Cos[t]-12Sin[t],2Cos[t],4Sin[t]},{t,0,2Pi},PlotStyle->Directive[Red,Thick]];
Show[p1,p2]