Question

The curve C is defined by the vector function: r(t) = 3ti + cos2tj + sin2tk....

The curve C is defined by the vector function: r(t) = 3ti + cos2tj + sin2tk. Find the Equations to the tangent line to the curve at the point P(0,1,0) corresponding to t=0. (please use a different parameter, say u, for tangent line)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3...
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t 2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space curve of r(t) at t = 3. (c) Find the vector equation of the tangent line to the curve at t = 3
20. Find the unit tangent vector T(t) and then use it to find a set of...
20. Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point. r(t)= -5t i+ 2t^2 j+3tk, t=5
4) Consider the polar curve r=e2theta a) Find the parametric equations x = f(θ), y =...
4) Consider the polar curve r=e2theta a) Find the parametric equations x = f(θ), y = g(θ) for this curve. b) Find the slope of the line tangent to this curve when θ=π. 6) a)Suppose r(t) = < cos(3t), sin(3t),4t >. Find the equation of the tangent line to r(t) at the point (-1, 0, 4pi). b) Find a vector orthogonal to the plane through the points P (1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a)...
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a) What is the vector representation r⃗(t) for C ? (b) Is C a smooth curve? Justify your answer. (c) Find a unit tangent vector to C . (d) Let the vector-valued function v⃗ be defined by v⃗(t)=dr⃗(t)/dt Evaluate the following indefinite integral ∫(v⃗(t)×i^)dt. (cross product)
Letr(t)=(4t2+1)i+2tjfor−2≤t≤2. (a) (10 pts) Draw a sketch of the curve C determined by r(t). (b) (5...
Letr(t)=(4t2+1)i+2tjfor−2≤t≤2. (a) (10 pts) Draw a sketch of the curve C determined by r(t). (b) (5 pts) Plot r(0) and label its endpoint P. (c) (10 pts) Plot the vector tangent to C at P . (d) (10 pts) Find the equation of the line tangent to C at P (you may give this parametrically or not). (e) (5 pts) Find the curvature K at P . (f) (5 pts) Find the radius of curvature ρ at P. (g) (5...
Determine the tangent line at point t = π/3 of the curve defined by the parametric...
Determine the tangent line at point t = π/3 of the curve defined by the parametric equations: X = 2 sin (t) Y = 5 cos (t)
At a given point on a smooth space curve r(t), T(t) is the unit tangent vector,...
At a given point on a smooth space curve r(t), T(t) is the unit tangent vector, N(t) is the principle unit normal vector and B(t) is the binormal vector. Which of the following are correct? (The multiple-choice question might have more than one correct answer. Circle all correct answers for full credit.) Group of answer choices A)None of the above has to be true. B) T ( t ) ⋅ T ′ ( t ) = 0 C) | B...
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
Find the unit tangent vector T(t) and the curvature κ(t) for the curve r(t) = <6t^3...
Find the unit tangent vector T(t) and the curvature κ(t) for the curve r(t) = <6t^3 , t, −3t^2 >.
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t +...
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a. Carefully make 2 sketches of the plane curve over the interval . (5 pts) b. Compute the velocity and acceleration vectors, v(t) and a(t). (6 pts) c. On the 1st graph, sketch the position, velocity and acceleration vectors at t=-1. (5 pts) d. Compute the unit tangent and principal unit normal vectors, T and N at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT