To prove that a vector $x(t)$ lies in a plane. Prove that vector $x(t)=t\,\hat{i}+\left(\dfrac{1+t}{t}\right)\hat{ j}+\left(\dfrac{1-t^2}{t})\right)\hat{k}$ lies in a curve.
   I am puzzled. Don't know how to approach it.

I would have used "x", "y", and "z" rather than "f", "g", and "h" but the point is valid.  This curve lies in the plane x- y+ z= 1.
(I am assuming that i, j, and k are the unit vectors in the x, y, and z directions, respectively, not "quaternions".)
