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c. For the given function r with unit tangent vector T(t) (from (a)), deter- mine N(t) = T(t) T' (t). d. What geometric properties does N(t) have? That is, how long is this vector, and how is it situated in comparison to T(t)?

c. For the given function r with unit tangent vector T(t) (from (a)), deter- mine N(t) = T(t) T' (t). d. What geometric properties does N(t) have? That is, how long is this vector, and how is it situated in comparison to T(t)?

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Plz solve c and d parts within 30 minutes will definitely upvote 

14. Consider the standard helix parameterized by r(t) = cos(t)i+sin(t)j +tk. a. Recall that the unit tangent vector, T(t), is the vector tangent to the curve at time t that points in the direction of motion and has length 1. Find T(t). b. Explain why the fact that |T(t) = 1 implies that T and T' are orthogonal vectors for every value of t. (Hint: note that T T = |T|² = 1, and compute[T.T.) c. For the given function r with unit tangent vector T(t) (from (a)), deter- mine N(t) = [T'(t) T'(t). d. What geometric properties does N(t) have? That is, how long is this vector, and how is it situated in comparison to T(t)?
Transcribed Image Text:14. Consider the standard helix parameterized by r(t) = cos(t)i+sin(t)j +tk. a. Recall that the unit tangent vector, T(t), is the vector tangent to the curve at time t that points in the direction of motion and has length 1. Find T(t). b. Explain why the fact that |T(t) = 1 implies that T and T' are orthogonal vectors for every value of t. (Hint: note that T T = |T|² = 1, and compute[T.T.) c. For the given function r with unit tangent vector T(t) (from (a)), deter- mine N(t) = [T'(t) T'(t). d. What geometric properties does N(t) have? That is, how long is this vector, and how is it situated in comparison to T(t)?
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