A. B. Let the position vecor be R(t) = (-t, 4 cos (2t), 4 sin(2t)). Compute the principal unit normal vector N(t). (-1,-8 sin(2t), 8 cos(2t)) √65 (-t, 4 cos(2t), 4 sin(2t)) √65 O C. (-1,-8 sin(2t), 8 cos(2t)) D. (0,- (cos(2t)),- (sin(2t))) E. (0,- (16 cos(2t)),-16 sin(2t)) 65

Q: 3. Sketch the vector-valued function r(t) = (sin(2πt), t, 3 cos(2πt)), indicating direction.

A:

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A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

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A: Given, the vector-valued function  to find:  the vectors  and  and the binomial vector  at .

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A: Given vector function is, r(t)=3cost i+4sint j

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A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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A:

Q: (1) The position vector r of a missile at any time t is given by r = tį + (8t – t)j where į and j…

A: Solution by using formulaes :

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A:

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A: Given the vector valued function R(t)=tan-1t i^+t1-t2j^+sin t2k^. We have to find the domain of…

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A:

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A:

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A: Let the functions be