Question

In: Math

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and...

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and unit normal vectors T(t) and N(t).

(b). Find the curvature k(t).

Solutions

Expert Solution


Related Solutions

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...
Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=
15. a. Find the unit tangent vector T(1) at time t=1 for the space curve r(t)=〈t3...
15. a. Find the unit tangent vector T(1) at time t=1 for the space curve r(t)=〈t3 +3t, t2 +1, 3t+4〉. b. Compute the length of the space curve r(t) = 〈sin t, t, cos t〉 with 0 ≤ t ≤ 6.
(1 point) For the given position vectors r(t)r(t) compute the unit tangent vector T(t)T(t) for the...
(1 point) For the given position vectors r(t)r(t) compute the unit tangent vector T(t)T(t) for the given value of tt . A) Let r(t)=〈cos5t,sin5t〉 Then T(π4)〈 B) Let r(t)=〈t^2,t^3〉 Then T(4)=〈 C) Let r(t)=e^(5t)i+e^(−4t)j+tk Then T(−5)=
If T1 and T2 are independent exponential random variables, find the density function of R=T(2) -...
If T1 and T2 are independent exponential random variables, find the density function of R=T(2) - T(1). This is for the difference of the order statistics not of the variables, i.e. we are not looking for T2 - T1. It is implied that they are both from the same distribution. I know that fT(t) = λe-λt fT(1)T(2)(t1,t2) = 2 fT(t1)fT(t2) = 2λ2 e-λ​​​​​​​t1 e-λ​​​​​​​t2 , 0 < t1 < t2 and I need to find fR(r). From Mathematical Statistics and...
compute the unit tangent vector T and the principal normal unit vector N of the space...
compute the unit tangent vector T and the principal normal unit vector N of the space curve R(t)=<2t, t^2, 1/3t^3> at the point when t=1. Then find its length over the domain [0,2]
Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the...
Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the definite integral of r(t) for 2 ≤ t ≤ 3 can you please provide a Matlab code?
Show the complete solution. Determine the unit tangent vector (T), the unit normal vector (N), and...
Show the complete solution. Determine the unit tangent vector (T), the unit normal vector (N), and the curvature of ?(?) = 2? ? + ?^2 ? – 1/3 ?^3 k at t = 1.
Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the...
Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t)   =    N(t)   =    (b) Use this formula to find the curvature. κ(t) =
FOR THE PARAMETRIZED PATH r(t)= e^tcos(πt)i+e^tsin(πt)j+e^tk a) find the velocity vector, the unit tangent vector and...
FOR THE PARAMETRIZED PATH r(t)= e^tcos(πt)i+e^tsin(πt)j+e^tk a) find the velocity vector, the unit tangent vector and the arc lenght between t=0 and t=1 b) find a point where the path given by r(t) intersects the plane x-y=0 and determine the angle of intersection between the tangent vector to the curve and the normal vector to the plane.
Integration of the vector function: F(t) =et.sin2ti + t2j + t2.e2tk
Integration of the vector function: F(t) =et.sin2ti + t2j + t2.e2tk
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT