1. Suppose that r(t) = (3 cos(3t) · t, 3 sin(3t), 5t). a. Determine the velocity, the acceleration and the speed for t = 7/2. b. Determine whether the angle between the velocity vector and the acceleration vector for t = T/2 is right, acute or obtuse. c. Find the vector equation of the tangent to the trajectory of r for t = T/2.

Q: 5) Given: r(t) =( 2t, t2, ) O Find parametric equations for the tangent line to the curve at t O…

A: Here the given vector is  r→(t)=2t,t2,t33 a) we have to find parametric equations for tangent line…

Q: (a) Find the position vector of a particle that has the given acceleration and the specified initial…

A: Solve the following

Q: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). %3D a. Determine the velocity, the acceleration…

A: For a position vector r(t), the velocity vector of the r(t)  is given by the first derivative of the…

Q: Given that the acceleration vector is a (t) = (-16 cos(-4t), – 16 sin(-4t), –t), the initial…

A:

Q: (b) ( s) Find the parametric equations of the tangent line to the curve x(t) = t° – t + 1, y(t) = t³…

A:

Q: Given the vector function (1) = (e+²³, 2√²³ +1, 4arctan(1 − 1)) 1)), find the speed and the equation…

A:

Q: Let 7(t) = (t + 4, – e*, 3 sin(3t)) - Find the unit tangent vector T (t) at the point t = :0 T(0) =

A: We have to find

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: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). a. Determine the velocity, the acceleration and…

A: For velocity vector diffrenciate displacement vector. And for acceleration vector diffrenciate…

Q: 2. Consider the function 7(t) = (t² - 4,t – 2,v80 + 4t + 7t? - t*). Find parametric equation(s) for…

A:

Q: Suppose r(t) = cos(nt) i + sin(t) j+ 3tk represents the position of a particle on a helix, where z…

A: Given the vector

Q: 5. Find the equation of the tangent line to the curve given by the parametric equations x(t)= 3r² –…

A: We are authorized to solve only 1 question, please repost remaining questions Equation of tangent to…

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

A:

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: 1. Find the tangent vector to the curve 6t r(t) = [t3 – t, (2t + 1)*] t+1 at t = 1.

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: 2. Suppose that the position of a particle is r(t) = (cos(nt), ² sin(nt), t), 0≤t≤ 2n. A. Calculate…

A: Understanding of derivative while finding velocity and acceleration from position vector is…

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

Q: The position vector of a moving point is given as :R(t)=(cos t)i+(sint) j+(t) k ; the distance…

A:

Q: Consider the following trajectory of a moving object. Find the tangential and normal components of…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: (a) Given: The electrical potential at point x,y,z ,Vx,y,z=5x2-3xy+xyz . Concept used: The rate of…

Q: At what times in the interval 0&lt;= t&lt;=pai are the velocity and acceleration vectors of the…

A:

Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

A:

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

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

A:

Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

A:

Q: Determine the velocity vector of the given path. r(t) = (6 cos?(t), 3t – t3, 2t)

A: We have to find the velocity

Q: a) Find the speed of the particle at t = 3, and find the acceleration vector of the particle at t =…

A:

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

A: We have acceleration, initial velocity, and initial position, and if we integrate acceleration with…

Q: Consider the following 3D trajectory: t p(t) = sin(2t) i +3 cos(t) j+ k 2n a. Calculate the position…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A:

Q: Example 1.9.8 Sketch the curve with the given vector equation. r(t) = sin(4t)i + tj + cos(4t)k.

A:

Q: Find the tangent, normal, and binormal vector functions for the following three curves:   1:…

A: We have to find the tangent vector, normal vector and bionomial vector function

Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

A:

Q: Given differential of the function f at the point (3,2) 2. df = 3dr + ddy Find the directional…

A:

Q: Given that r (t) = (5t cos 2t) j- (5t sin 2t) k, is the position vector of a moving particle, find…

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

A:

Q: Find the vector equation of the tangent line to F(t) = 2 (e-) in t i+ tan-tj+ the point where t = 1.…

A:

Q: Find the equation of the tangent line to the following parametric equation at the given point. x =…

A:

Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

A:

Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: Consider the following trajectory of a moving object Find the tangential and normal components of…

A:

Q: В. Given that r (t) = (3t cos t) j – (3t sin t) k , is the position %3D vector of a moving particle,…

A:

Q: Question 13 at t 1. Find the velocity, speed. and acceleration of the vector-valued function Kt) =…

A:

Q: C) If R(t) = (In(t2 + 1)i + (tan-t)j + (VE +1)k, is the position vector of a particle at time (t).…

A: