I'm currently studying for my calc 2 midterm and came across this and it completely lost me. I'm not even completely sure where to begin with it. Any ideas?
Put $\langle x[r,t],y[r,t],z[r,t] \rangle = \langle 1,0,1 \rangle + \langle r \cos[t],r \sin[t],0\rangle$. Describe what you get when you plot $\langle x[r,t],y[r,t],z[r,t] \rangle$ for $0\leq r \leq 2$ and $0\leq t \leq 2\pi$ .
Is this a curve or a surface?
Put $\langle x[t],y[t],z[t] \rangle = \langle 1,0,1 \rangle + \langle 2 \cos[t],2 \sin[t],0 \rangle$. Describe what you get when you plot $\langle x[t],y[t],z[t] \rangle$ for $0\leq t \leq 2\pi$.
Is this a curve or a surface? What relation does it have to what you said immediately above?