Find T, N, and B for the given space curve.r(t)= (6+t)i + (2 + In (sec t))j- 3k, - T/2

Find r'(t) by differentiating r(t) with respect to t. r(t)=6+ti+2+lnsec tj-3kr'(t)=i+sec t·tan tsec…

Answered: Find T, N, and B for the given space…

Math

Algebra

Find T, N, and B for the given space curve. r(1)= (6+t)i + (2 + In (sec t))j-3k, - T/2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 10RE

See similar textbooks

Related questions

Q: 3) Consider the curve C in R³ given by: r(t) = (t + In t, t – In t, 4t'/²) con 1<t< 2 An expression…

A: Formula: If r(t)=x(t), y(t), z(t), a≤t≤b is parametrization of a curve C then the line integral…

Q: Sketch the space curve and find its length over the given interval r(t) = ⟨8 cos t, 8 sin t, t⟩,…

A: Given Finding the derivative with respect to t:

Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…

A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…

Q: Find T, N, and k for the space curve r(t) = (12 sin t) i + (12 cos t) j+ 16t k. T(t) = () j+ k

Q: Find the minimum distance from the point P with coordinates (1. 2. 1) to the line r = a+Ab, where a…

A: The minimum distance from the point P(1,2,1) to the line r is the perpendicular distance between P…

Q: Q2/ Find T, N, and k for the space curve r(t) = (3 sin t)i +(3cos t)j + 4tk

A: Question: Objective is to calculate the tangent vector T, normal vector N and the curvature κ of…

Q: Find T, N, and k for the space curve r(t) = - 2e cos t)i- (2e sin t) j+ 2k.

Q: A possible way for the parameterization of the curve C corresponds to: (9t – t² A) r(t) = , t, z(t)…

A: In the three dimensional system, a parameter(usually "t") is used to describe the variables x, y and…

Q: Find T, N, and k for the space curves r(t) = (6 sin 2t)i + (6 cos 2t)j + 5tk

Q: 眼,。。。,,眼,。 a2f, a?f dy² ™ əz² + Эх2 " ду? + + əx² ERectively in ths plane and in the…

A: Given function is f(x,y)= e^-2y cos2x

Q: Find T, N, and k for the space curve, where t>0. r(t) = (8 cos t+ 8t sin t)i + (8 sin t- 8t cos t)j+…

Q: Sketch the plane curve r(t) = t2i − 4tj and find its length over the given interval [0, 5] .

Q: Find T, N, and k for the space curve, where t> 0. r(t) = ( cos t+t sin t)i + ( sin t-t cos t)j + 4k

Q: 7. Given the space curve er(t) = (4 sin t ,4 cos t , 10t), Find T, N, B, and t (torsion)

Q: In which of the following cases the circle T NS has radius R = 2 and center C = (1,-1,0)? %3D O (a)…

A: To solve the following problem

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk

A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk To determine: The values of the unit…

Q: Sketch the plane curve r(t) = t3i + t2j and find its length over the given interval [0, 1] .

Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=

A: The value of the given function can be found with the help of the integration. Substitution of…

Q: 4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is…

A: (4) To find: f such that F→=∇f and To Evaluate: ∫CF→·dr→. For the following Functions: (a)…

Q: Find T(t), N(t), aT , and aN at the given time t for the plane curve r(t) r(t)=(t-t3)i+2t2j, t=1

A: The solution is given as follows

Q: Find T, N, and x for the space curve r(t) = (6e'cos t) i + (6e'sin t)j+ 4k. T(1) = Di+Oi+k (Type…

A: Given r→t=6etcosti^+6etsintj^+4k^ We have to find the T, N and κ for the given curve. Differentiate…

Q: 2. Let L be the line tangent to the space curve represented by r(t) = (t² – In(t))i+(e²-t – t)j+…

Q: (a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk x² + y? <…

Q: Let f(r, y, 2) = 2ry + 2. Evaluate f(1, y, 2) dz where C is the portion of the helix r(t) = cos ti+…

Q: 2. Let F(t) = (e' cos t) î+ (e' sin t)j+ek. a. Find symmetric equations of the line tangent to the…

A: Given: F→t = et costi^ +et sint j^ +et k^ To Find: Symmetric equations of the line tangent to the…

Q: Find T, N, and K for the space curve r(t) = (9 sin t) i + (9 cos t) j+ 12t k. T(t) = (O i+ O i+ (O k

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j+ 7R, 0 st s 3.…

Q: Find a piecewise smooth parametrization of the path C. 0 st<1 (ti+tj r(t) = %3D 1<t<2 (1, 1) y=x

A: Given rt=ti + tj 0≤t≤1 1≤t≤2

Q: = Let Co be the curve formed by the intersection of the surfaces x₁ = 2x² and X3 3x1x2, and let C be…

Q: Determine whether the space curve given by r(t) =t 2, t 2− 2t − 3, t − 3 intersects the x-axis, and…

Q: Let C be the curve parameterized as follows F(t) := (9 cos(t), 9 sin(t), 12t), 0<ts 10 and let f(x,…

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j + 9k, 0 < t s…

Q: Find T, N, and k for the space curve, where t> 0. r(t) = (2 cos t+ 2t sin t)i + (2 sint- 2t cos t)j…

Q: 1. Sketch each curve in the z-plane, and sketch its image under w = 2². (a) |z1|=1 (b) x = 1 (e) y²…

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

Q: 3. Sketch the space curve, r(t) = 8 cos ti +8 sin t j+tk , and find its length over the interval []…

A: Given: r(t)=8cost+8sint+tk [0,pi/2]

Q: Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: (5) Determine whether Fř is independent of the path when C is any closed curve and (i) F(x, y, z) =…

A: Here we use the curl of vector function to determine its dependency on the closed curve as follows

Q: Find T, N, and k for the space curve r(t) = (16 sin t) i + (16 cos t) j+ 12t k. T(1) = (D i+ (O j+…

Q: (b)for the space curve,r(t) = costi + sintj + tk, 0st< 4n

Q: Let c be a smooth curve defined by r(t)= with 1

Q: 12. Let T be the line tangent to the space curve represented by r(t) = (t³ + e=t )i+ (ln(t) + 2t )j+…

A: First we find the equation of tangent in Cartesian form, and then check whether the tangent…

Q: A) Find B and t for the space curve r(t): = (3 sin t)i + (3 cos t)j + (t)k.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question…

Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given Data: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is…

Q: 1.108. Find F•dr where F = (z - 3y)i + (y - 2x)j and C is the closed curve in the zy plane, z = 2…

A: We have to find ∮CF·dr where F=x-3yi+y-2xj and C is the closed curve in the xy-plane. x=2cost,…

Q: 8 Find T, N, and k for the space curve r(t) = Gi+gj, t> 0 8

Q: A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0.…

A: Given: →γ(t);t1≤t≤t2→(τ);τ1≤τ≤τ2β To find: a) Prove that ∫t1t2→γ'(t)dt=∫τ1τ2→β'(τ)dτ. b)…

Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

Q: Find T and N for the given space curve. (1) = (10 + t) i + (4 + In(sec t)) j – 10k; Upload Choose a…

Q: (b) Find the curvature for the space curve r(t) =(1.",)at the point.1.11 using the formula 10.

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Find T, N, and B for the given space curve.
r(t)= (6+t)i + (2 + In (sec t))j- 3k, - T/2 <t < T/2
O A. T-(cos t)i + (sin t)j; N = (- sin t)i + ( cos t)j, B = k
O B. T=(- cos t)i - (sin t)j; N=(sin t)i – (cos t)j, B = - k
Oc.
O C. T= (- cos t)i - ( sin t)j;N = (- cos t)i +(sin t)j, B = k
O D. T-(cos t)i - (sin t)j; N=(- sin t)i - (cos t)j. B = - k

Expert Solution

Step 1

Find $r' (t)$ by differentiating $r (t)$ with respect to t.

$\begin{array}{rcl} r (t) & = & (6 + t) i + (2 + \ln (sec t)) j - 3 k \\ r' (t) & = & i + (\frac{sec t \cdot \tan t}{sec t}) j - 0 k \\ = & i + (\tan t) j \end{array}$

Now, find $||r (t)||$ . Use the identity $1 + \tan^{2} θ = {sec}^{2} θ$ .

$\begin{array}{rcl} ||r (t)|| & = & \sqrt{{(1)}^{2} + {(\tan t)}^{2}} \\ = & \sqrt{1 + \tan^{2} t} \\ = & \sqrt{{sec}^{2} t} \\ = & sec t \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector-valued Function$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.