Find the curvature of the space curve. 1) r(t) - - 61+ (t + 10)j +(In(cost) + 6)k
26. What is the angle between the tangent to the curve R(t) = ti + 1?j + 2tk (Osts 3) and the normal to the surface z = 16 – x2 – y at their point of intersection?
Find the curvature of the space curve. r(t) = -21 + (7 + 2t)j + (t2 + 5)k Ok=- 1 2012 Ver I 1 K= 2(2 + 1)3/2 Ok= 1 (2 + 1) 3/2 Oku- 1 2012-132
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(sect))j-9k, Find the tangential and normal components of the acceleration for the curve r(t)-(t2-5)i + (21-3)j +3k. 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
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
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
Plane Curves Find T, N, and K for the plane curves in Exercises 1-4 1,/r(t) ti (In cos j, /2 <t< T/2
Find the curvature of the space curve. r(t) = -5 i + (10 + 2t)j + (t? + 8) k Ov-2021 2052 or OK 2(+1312
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...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.) X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...