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

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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Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

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Question Posted: Jan 16, 2024 03:01 AM

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

Question:

XXoy- Yo = xo Yo z - Zo zo

Step by Step Answer:

The direction ...View the full answer

Modern Engineering Mathematics

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