Given the following parametric equation of a space curve: (a) sketch the curve, (b) find the equation of the tangent line at the point P with t = π/3, (c) find the equation of a plane orthogonal to...

Given the following parametric equation of a space curve:

(a) sketch the curve,

(b) find the equation of the tangent line at the point P with t = π/3,

(c) find the equation of a plane orthogonal to the curve at P,

(d) show that the curve lies in the surface