Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(3t)) when t 3 Velocity: Acceleration: Speed:

Q: Q2:- A/ Given a position vector: R (t)= 3 cos ti+3 sin tj+ t2 k find 1- The velocity vector and…

A:

Q: Suppose you are given a vector-valued function modelling the velocity of a particle in space. At…

A:

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: Find the directional derivative of the function f (x, Y, z) = 6x² –- 2xy + yz in the direction of…

A:

Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

A:

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

A: Topic - vectors

Q: Find a unit vector in the direction in which f (x, y) = 8 cos(5x – 3y) decreases most rapidly at P…

A:

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

A: Given  a t=4t,5 sint, cos 3twe know that,v→t=∫a t dt +C1r t=∫vt  dt  +C2 ∴v→t=∫4t, 5 sint, cos 3t…

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(9 + sin t) and 0 = 3 - e',…

A:

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

A:

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

Q: Find the velocity vector for the position vector r(t) = (sin(12t), 8t°, e-6*). x component = y…

A:

Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

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

A:

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

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

A:

Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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: An object is spinning at a constant speed on the end of a string, according to the position vector…

A:

Q: Find the vector equation of the tangent line to F(e) = 2 (e1-t) in t i + tan"1tj+ k at cos(t ) the…

A: To determine the vector equation of the tangent line.

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

A: We have to find r(t)

Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

A:

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

A:

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

A:

Q: Find a unit vector in the direction in which f(x, y) = 6 cos(x – 5y) decreases most rapidly at P and…

A: Given, fx,y=6cosx-5y Find the unit vector and rate of change of f at P.

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(3t), cos(t), sin(t)) when…

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

A:

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

A:

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

A:

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: Let r(t) = (sin 2t ,3t, cos 2t), -n SIST, a) Is speed always constant? b) Show that the velocity and…

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(7 - cos 0) and de =7, where a…

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(6 + cos t) and 0= 5+ e where…

A:

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object

Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

A:

Q: and ue. Find the velocity and acceleration vectors in terms of u, r= 5 sint and 0 = 8t

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= a(7- sin 0) and =7, where a…

A:

Q: Find the velocity and acceleration vectors in terms of u, and ue. de = 4t, where a is a constant dt…

A:

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

A:

Q: p1. Find the directional derivative of o = x²z+ 2xy² + yz? at (1, 2,-1) in the direction of vector…

A: on using gradient we get

Q: Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

A:

Q: Find the directional derivative of the function f(x, y) = In(at + y) at the point (- 1, - 2) in the…

A: