a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2<t<π/2. r(t) = (4 + t)i-(8+In(sec...
(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 >.
(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
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that all of your answers should be numbers (1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K...
(1 point) Given R' (t) R' (t)ll Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t)- N(t) (1 point) Given R' (t) R' (t)ll Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t)- N(t)
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
5. Find the unit tangent vector T(t), the unit normal vector Nt), and the curvature k(t) for the vector function r(t) = (3t, cost,-sint).
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)-- EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (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 >.