Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make with a horizontal line in the positive direction?

Q: Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (6, 36).

A: The parabola y = x2 and the point (6, 36)

Q: Find unit tangent vector of the curve r=(2+t)i-(t+1)j+k

A: In this question, we need to find the unit tangent vector of the given curve.

Q: 2. Find the unit tangent vector for the curve r(t) = (t cost, tsin t).

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Q: Find the directional derivative at (1,0) if Vƒ(1,0) = in the direction of the unit vector u = i?…

A: Given : ∇f(1,0)=<-4,3>   To Find: directional derivative at (1,0) in the direction of the unit…

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: Find the unit tangent vector to the curve at the specified value of the parameter. r(t): = 7 cos(t)i…

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Q: A unit tangent vector to the curve r(t) = [sin(t), cos(t), 2f] at the point A:(0, — 1, 2п) is given…

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Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

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

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= a(4+ sin t) and 0 =9- e -t,…

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Q: Show that at every point on the curve r (t) = ⟨et cos t, et sin t, et⟩ the angle between the unit…

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Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

A: Consider that: rθ=sin θ, cos θ, cos 3θ at θ=π3. Velocity vector denoted by vθ is vθ=r'θ.  Calculate…

Q: Find the tangential and normal components of acceleration for the position vector denoted by 7 = (t…

A: We have given position vector  t+29,2t,t2 Then, Tangential component of acceleration aT=r't.r''tr't…

Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. .…

A: Given:                  rt=cos3tj+sin3tk,     0≤t≤π2                 v=ddtrt=ddtcos3t j+sin3t…

Q: How would I find the unit tangent vector T(t) at the point with the given value of the parameter t.

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Q: Find the acute angle that a constant unit force vector makes with the positive x-axis if the work…

A: Given- a constant unit force vector makes with the positive x-axis if the work done by the force in…

Q: Show that at every point on the curver(t) = ⟨et cos t, et sin t, et ⟩ the angle between the unit…

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Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: Suppose that C has length 5. What is the value of F. dr if: (a) F(P) is normal to C at all points P…

A: Given: Length of C is 5. (a) F(P) is normal to C at all points P on C. ∫CF→·dr→=∫CFdrcos90°=0…

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

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Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: Find the angle 0 (in radians) between the vectors. u = cos + sin v = cos 4 + sin 4

A: Given, u=cosπ4i+sinπ4jv=cos5π4i+sin5π4j

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

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Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 20 and 5t, where a is…

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Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

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

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r=5 sint and 0= 5t = (5 cost) u, +…

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Q: Write down the vector equations of the tangent lines to the traces for /(r, 3) = re-y² at (2,0) for…

A: To write the vector equation of the tangent line for the below function to the trace y=0.…

Q: Find a unit tangent vector to any point on the curve x = a cos wi, y = a sin wt, z = bt where a,b,w…

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

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Q: Find the velocity and acceleration vectors in terms of u, and ue. r=7 sin 3t and 0= 9t 3Du, +ue V =…

A: Given To determine  the velocity and acceleration vectors

Q: If the vector ? has constant magnitude, then show that the vector? and vector dA/dt are…

A: To show that the vector A and the vector dA/dt are perpendicular.Consider A.A = A2cos(0) = K(a…

Q: A ship is sailing at a speed of 14 mi/hr in the direction S50°E. Express its velocity v as a vector.

A: A ship is sailing at a speed of 14 mi/hr in the direction S50°E. Express its velocity v as a vector.…

Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

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

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. (-)- II r(t) = 3…

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Q: How do you find the Unit Tangent Vector to a curve C when you are given x(t) and y(t)? Where you are…

A: Suppose we are given a smooth curve C:r(t)→=<x(t),y(t)>on an openinterval I. Then a unit…

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

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Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3tk T(pi/2) = %3D…

A: Here the given vector is  r→(t)=e3t cos(t) i+e3t sin(t) j+e3t kr→(t)=e3t cos(t) , e3t sin(t)  , e3t…

Q: Find the unit tangent, normal and binormal vectors T, N and B for the curve at the point (0, 7, -1).

A: The curve is defined by the vector function rt=sint2,t2,cost2 on the domain [0,∞) To find the unit…

Q: The unit tangent vector of a(t) =cos 2t e, +stn 2t e, - tez at t = is

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

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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: For the function f(x,y)=(4−x^2−y^2)/−5, find a unit tangent vector to the level curve at the point…

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

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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: Find the velocity vector for the position vector r(t) = (sin(3t), 10t°, e -"). x component = y…

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