(1 point) Find a vector equation for the tangent line to the curve r(t) = (2/)...
x = COST TT 7) Find the slope of the line tangent to at t = y = 8 sint 2 1 -" 3 8) Find the length of 0<t<1 1 - 21
(b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
The component-form equation for the equation of the line through the point (1,0,1) and perpendicular to the vectors <3.5,2> and <2.1.0> is F(t) = (1 + 2t, 4t, 1 - 7t) • F(t) = (1 + 2t, -4,1 - 7t) F(t) = (1+2t, t, 1) F(t) = (1 +3,5t, 1-2t)
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
13.4.1 TT ht Find T, N, and k for the plane curve r(t) = 2+ i +2 In (cost)j, - 3<t<z
The answer above is NOT correct. (1 point) Find the length of the curve r(t) = i +3t'j + t'k, 0 <t</45 L Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a score of 0% for this attempt. Your overall recorded score is 0%. You have unlimited attempts remaining. Email WebWork TA WebWork 1996-20
Let r(t) = <cos(5t), sin(5t), v7t>. (a) (7 points) Find |r'(t)|| (b) (7 points) Find and simplify T(t), the unit tangent vector. Upload Choose a File
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the line integral S ry ryds. 1/V2. 1/2, V2, 0,
a) Find the length of the curve traced by the given vector function on the indicated interval: r(t)e' costie' sin tj+e'k 0<t<In2 b) Find the gradient of the scalar function f 6xyz + 2x+ xz at (1, 1, -1) c) Find the curl of the given vector field: F(x, y,z) 4xyi + (2x2 +2yz)j+(3z2+y2)k