Find three different surfaces that contain the curve r (t) = t^2 i + lnt j + (1/t) k

solution:

Consider the curve: r (t) = t²i + (int) j + 1/t k

X = t², y = int, z = 1/t

Using, x = t², z = 1/t

X = (1/z) ²

Xz² = 1

Using y = int, z = 1/t

Y = in│1/z│

Using x = t², y = int

Y = int

= in (√x)

Hence, the required surface are,

Xz² = 1

Y = in│1/z│

Y = in (√x)