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3. The parametric curve ~r1(t) = 4t~i + (2t − 2)~j + (6t 2 − 7)~k...

3. The parametric curve ~r1(t) = 4t~i + (2t − 2)~j + (6t 2 − 7)~k is given.

(a) Find a parametric equation of the tangent line at the point (4, 0, −1)

(b) Find points on the curve at which the tangent lines are perpendicular to the line x = z, y = 0

(c) Show that the curve is at the intersection between a plane and a cylinder

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