QI/ Find the curve unit tangent vector and length of the indicated portion of the curve rt) = (9 sin 21i + (6cos 21)j + 5t k urve

Q: 7. Eliminate the paramet er to find a Cartesian equation of the curve, x = sin t, y = csc t, 0 < t <…

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Q: Arc length: Find the length of the space curve with vector equation r(t) =(4, 3cost, 3 sint ) over […

A: We have to find the arc length.   According to our guidelines we can do only one question so please…

Q: Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval…

A: To eliminate t and find cartesian equation.

Q: A particle is moving in the velocity of v(t) = . %3D Find the unit tangent of the particle's…

A: Given- vt=&lt;9sint, 9cost,4&gt; To Find- The unit tangent of the particle's movement.

Q: Find equations of the tangent plane and normal line to the surface z + 19 = xe cos z at the point…

A: We have to find tangent plane equation and normal line.

Q: Find the equation of the tangent plane and the normal line to the given surface at the specified…

A: Given:- 24z/x+x3y4+8ysin(z) -2048 To find:- Find the equation of tangent plane and normal line at…

Q: QI/ Find the curve unit tangent vector and length of the indicated portion of the curve rt) = (9 sin…

A: Given information: The curve of the function rt=9sin2ti+6cos2tj+5tk. Unit tangent vector can be…

Q: e curve's unit tangent vector. Also, find the length of the in cos ) j+ (3 sin 31) k, Osts . e…

A: here we have to find the unit tangent vector , also find the length of indicated portion of the…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Equation of the tangent plane to the surface 7(u,v) at (uo,Vo) is given by 7-7(uo, Vo)]× Ñ(uo,Vo)…

A: To find: Equation of the tangent plane to the surface r→u,v at u0,v0

Q: Find parametric equations for the tangent line to the curve with the parametric equations x…

A: Given: The parametric equations, x = t2+3,  y = ln t2+3, z = t and the point 2, ln4, 1. To find: The…

Q: Find parametric equations for the tangent line to the given curve at the point (30, 135, 469). The…

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Q: A parametric curve C is given by the position vector F(1)=sin(21). sin" (+),e' osis Osis". a) Find…

A: a)The given position vector is, r→(t)=12sin(2t),sin2t,et

Q: (a) Find parametric equations for the tangent line to the curve -tcost, y-t, -tsint at the point…

A: We have to find parametric equations for given point-

Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x^2 at point (2,…

A: y=x2 at point (2,4) We need to find the unit vectors that are parallel to the tangent line to the…

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: Find the second derivative of y with respect to x from the parametric equation given. Plot the curve…

A: Given that,  x=3+4sinθ ,    y=3cosθ-4 We need to find the value of d2ydx2

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost…

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Q: Find parametric equations for the tangent line to the curve r(t) = at the point (1,0,1)

A: Introduction: A line that barely touches a curve (or function) at a specific location is said to be…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A:

Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

A: (a) Given  parametric form of curve is…

Q: t. A projectile is fired from a height of 8.2 feet with an initial velocity of 122 ft/sec at an…

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Q: please find the normal plane equation and parametric equations for the tangent line to the curve…

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Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

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Q: Find parametric equations for the tangent line at the point (cos(), sin(²), ) on the curve x = cos…

A: Given query is to find the parametric equation of the tangent.

Q: Find the unit tangent vector T(t). r(t) = (5 cos t, 5 sin t, 8), PG 8) Find a set of parametric…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: A Hermite cubic spline starts at point (0, 0, 1) and ends at point (1, 2, 3). The tangent vectors at…

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Q: Find the tangent line in the x direction, l_x(t). b. Find the directional tangent line, l_u(?),…

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Q: Find parametric equations for the tangent line at the point (cos(), sin(5 ), ) on the curve a = cos…

A: Here, the given parametric equation of the curver(t)=(x,y,z) where x=cos t, y=sin t, z=t. To find…

Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x +…

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Q: Please show your answer to 4 decimal places. Find the direction in which the maximum rate of change…

A: Note:-   Maximum rate of change of f(x,y) at (a,b) occurs in the direction   ∇f(a,b).

Q: Find the second derivative of y with respect to x from the parametric equations given. Pls show the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Questlon a.- Fad the parametric form of the Curve x =a Cos (-)-Jy (zaryo Curve is a reqular Curve…

A: To find the parametric form of the curve,

Q: Two parametric equations are given by: x = cos (1), y sin (t) u- sin(t) v - cos(t) In one figure,…

A: Any point in the cartesian coordinate system is defined as x,y. The parametric functions are defined…

Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at…

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Q: Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: make a table values t x=t+sint y=cost -π x=-π +sin-π=-π +0=-π =-3.14 y=cos-π=-1 -π2…

Q: Find an equation of the tangent plane to the given surface

A: The given equation is z = x sin(x+y) at (-1,1,0)

Q: Find the points (x, y) at which the polar curve r = 1 + sin(0), – < 0 has a vertical and horizontal…

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Q: Find set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: quations for the tangent plane and normal line at the poi

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Q: Find parametric equations for the tangent line at the point (cos(), sin(), ) on the curve z = cos t,…

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Q: Find the unit tangent vector T(). Fed a set of parametric equations for the line tangent to the…

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Q: Find parametric equations for the tangent line to the curve x=2 sin t, y= 2 sin 2t, z=2 sin 3t at…

A: To find -

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given  x=e-3tcos8ty=e-3tsin8tz=e-3t

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: The given curve is -rt=lnt4i∧+t-4t+θj∧+t Ln t4k∧ - 1     t=to=4differentiating 1wrt t , we get…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: The surfaces are provided as z=x2+y2, z=16-y. We need to determine the set of parametric equation…

Q: A force F, measured in Newtons, is given by F = 2i + j+ 2k. Point C is located at (1, –2, 3), and…

A: Given  F⇀=2i⇀+j⇀+2k⇀ Along with CD: The particle displacement ds=dxi⇀+dyj⇀+dz k⇀ Then the net work…

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.