
4. Let point P(2,1,12) and Q be points on the curve r(t)=(5- 3t, 4t – 3,12t)....
4. Let point P(2,1,12) and Q be points on the curve r(t)=(5- 3t, 4t – 3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.
4. Let point P(2,1,12) and Q be points on the curve r(t)= (5 – 31,4t – 3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.
4. Let point P(2,1,12) and Q be points on the curve r(t)=(5 – 31,4t – 3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.
4. Let point P(2,1,12) and Q be points on the curve r(t)=(5-31, 41-3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 2t i + (2 − 3t) j + (8 + 4t) k r(t(s)) =
Find the curvature of the curve r(t) = (3 cos(4t), 3 sin(4t), t) at the point t = 0 Give your answer to two decimal places Preview
X 14.1.43 Find the point (if it exists) at which the following plane and curve intersect. z = 9; r(t) = (t, 4t, 3 + 3t), for -20 <t<oo Select the correct choice below and, if necessary, fill in the answer box to complete your answer. O A. The point at which the plane and line intersect is (Simplify your answer. Type an ordered triple.) OB. The curve and the plane do not intersect.