Find the parametric equations of the tangent line to the curve represented by the vector function 7 (t) = (t – 7, –3t? – t – 3, 3ť² + 2t +5) at the point (-5, -17,21).

Q: At which point P does the curve r(t)=( 2t, 4t+1, t’) given in vector form have the tangent vector…

A: Given: To explain the correct option of the given statement as follows,

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

Q: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

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Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. t,4t 2,2t 3),…

A: Differentiation: The line must pass through the point at t=-2 is  (t,4t+2,2t+3)=(-2,-6,-1)

Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: Find the set of parametric equations for the tangent line to the graph of the vector-valued function…

A: To find the set of parametric equations for the tangent line to the R(t)=<t+sin3t, t+cos3t,…

Q: Find all values of t for which the tangent line to the curve r(t) = (2t – t,t - t²) is orthogonal to…

A: Find the solution below

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

Q: If an object follows the path of the two-dimensional vector-valued function p(t)=(16−cos(t),…

A: Given p(t)=(16−cos(t), 0.6πt−0.15t2−3)

Q: Sketch the curve represented by the vector-valued function                              r(t) = (t +…

A: Given: The vector-valued function  r(t) = (t + 1)i + (3t − 1)j + 2tk and it gives the orientation of…

Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

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Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: At which point P does the curve r(t) =( 2t2, 4t+1, t³ ) given in vector form have the tangent vector…

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Consider the curve C parameterized by f(t)=(t^2+2t+3,-2t-4,t^2-1),t E [0,+infinite[ a)Find the plane…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We will use integration to go toward position fro acceleration

Q: At which point P does the curve r(t) = ( 21°, 21°, 3t – 1) given in vector form have the tangent…

A: Given r→(t) = 2t3 , 2t2 , 3t-1 Then r→'(t) = 6t2 , 4t , 3 Tangent vector at a point is given as 24 ,…

Q: At which point P does the curve r(t) = ( 21?, 4t +1, t) given in vector form have the tangent vector…

A: Given equation of curve as, r→(t)=2t2,4t+1,t3.

Q: Find the unit tangent vector of the given curve. r(t) = (7- 2t)i + (2t - 3)j + (6 + t)k 2 1 O A.…

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Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

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Q: Find the tangential and normal components of the acceleration vector for the curve F(t) = (t²,…

A: Here we have to find the tangential and normal components of the acceleration vector for the curve…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: At which point P does the curve r(t) = ( 2t2, 4t +1, t³ ) given in vector form have the tangent…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Finding the Position Vector for a Particle: The integration of the acceleration vector is the…

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

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Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: For time >0, the position of a particle moving in the xy-plane is given by the parametric equations…

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Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

Q: Find the unit tangent vector r(t) = t2i + tj + 4/3k and a set o f parametric equations P(1, 1, 4/3)…

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w =…

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Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: At which point P does the curve r(t) = ( 2t+3, 3t², t* ) given in vector form have the tangent…

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Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =…

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function.…

Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

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Q: Given the vector function r(t)=(1−t³, 3t+1, 4+1²), the equation of the tangent parabola/quadratic to…

A: We have to solve given problems:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We have to find position vector

Q: Find the position vector for a particle with acceleration, initial velocity, and tinitial position…

A:

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

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Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

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Q: At which point P does the curve r(t)=( 2t³, 21², 3t – 1) givenin vector form have the tangent vector…

A: According to the problem, we have

Q: G. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

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Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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