i) Show that the  curve α is unit speed,

Q: Sketch the plane curve represented by the vector valued function, and give the orientation of the…

A: To Sketch the plane curve represented by the vector valued function Give the orientation of the…

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

A:

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Given the vector function: *(t) = (1+ sin (3t), tan (2t), t) Relate the vector functions to the…

A:

Q: (b) Suppose that the position vector of a particle moving in the plane is r-12vii+j, t>0. Find the…

A: This is application of derivative problem

Q: A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the…

A: Start from the origin, move p units to the right along the x axis and q units up along the y axis to…

Q: Find the principal unit norma l r(t) = 6 cos ti + 6 sin tj + vector to the curve at the specified…

A: Given: r(t) = 6cost i + 6sint j To Find: Principal unit normal vector of the given position vector…

Q: 5Let MH)=Hit2costj + (2shnt-3k a) Find unit tingent vector TH) of rtH)

A:

Q: 6. Compute the Divergence and Curl of the following vector F:F = yze#vi + xze#¥j+(e™y + 3 cos 32)k…

A: Use divergence and curl formula Compare hyperbola with standard equation of hyperbola

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

A:

Q: give the position vectors of particles moving alongvarious curves in the xy-plane. In each case,…

A:

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

A:

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: Consider the curve defined as r(t) = e^ti + e^tj + t k Determine the point on the curve where the…

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: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: Q1:- Find the domain of the following vector fumctions:- (a) f(t) = (cos nt)i - Ln(t)j + Vt-2k (b)…

A:

Q: Find the arc length of the vector curve 7(t) = (2t, t², (1/3)t³), 0<t< 2.

A: Find the arc length of the curve

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

A:

Q: Find the vector r' (to); then sketch the graph of r (t) in 2-space and draw the tangent vector r'…

A:

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

A:

Q: Find the binormal vector, curvature and radius of curvature for the vector function r=3 cos 3ti +…

A: The radius of curvature is the reciprocal of the curvature which is reciprocal of Kapha is the…

Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: The angular velocity vector, ω, can be obtained by adding all components of the angular velocities…

A: Given, Angular velocity vectorω as the addition of all angular velocities. To find: To choose the…

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

A: Given,

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

A:

Q: Show that if r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies…

A: If r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies on a sphere…

Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not…

A:

Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by &lt; t^2+1, ln(2t+3) &gt; for all t&gt;=0

Q: A particle moves through 3-space in such a way that its acceleration is a(t) = 8sin 2ti +8 cos…

A:

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve = (3…

A:

Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: Find the (a) velocity vector, (b) speed, and (c) acceleration vector for the particle that moves…

A: rt=2sint2 i+2cost2 j a). Velocity vector is the derivative of position vector. That is,…

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: A velocity vector of v = 3t2i − 6t3 j − 4K ft/s  is governing the movement of an object in the 3D…

A: It is given that v=3t2i-6t3j-4kfts. Also, object starts at -1,4,5 at t=0. That is, s0=-i+4j+5k.…

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

A:

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A:

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

A: We have to find position vector

Q: Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

A: Given the curve  r→(t) = i→ + 2ln(t)j→ + 1tk→

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

A:

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

A:

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A: First we have to complete the required step by using the correct expression for torque.

Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…

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

A: The given vector equation is

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

A:

Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

A: