A curve C in three dimensions is given parametrically by (x(t), y(t), z(t)), where t is a

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A curve C in three dimensions is given parametrically by (x(t), y(t), z(t)), where t is a real parameter, with a ≤ t ≤ b. Show that the equation of the tangent line at a point P on this curve where t = t0 is given by

XXoy Yo - = xo Yo z - Zo zo

where x0 = x(t0), x´0 = x´(t0), and so on. Hence find the equation of the tangent line to the circular helix

x = a cost, y = a sint, z = at

at t = 1/4π and show that the length of the helix between t = 0 and t = 1/2π is πa/√2.

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