Starting from the point (-3, –1, 1) reparametrize the curve r (t) = (-3+ 3t) i+(-1+2t)j+ (1+ 3t) k in terms of arclength. r (t (s)) = i+ j+ k
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A: We need to reparametrize the given curve in terms of arclength. The solution is given below.
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A: Let's reparameterize vector value function R(t).
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- Starting from the point (3,−4,−2) reparametrize the curve r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k in terms of arclength. HINT. Your result should be the position of the "particle", which moves along the curve, after traveling distance s from the initial point.Starting from the point (1, −7, 0), the re-parametrization of the the curve r(t) = (1 + 3t)i + (−7 + t)j + (−√(6)t)kin terms of arc length isConsider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)]Compute the arclength function s(t): (with initial point t=0).
- Parametrize a circular spiral centered at the z-axis, starting at (0,2,0) and ending at (0,2,12) after four turns counterclockwise for 0 <= t <= 1 and find its length.Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.A particle moves in the xy-plane with position given by (x (t), y(t )) = (5 - 2t,t2 - 3) at time t. In which direction is the particle moving as it passes through the point (3, -2) ?