Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² + 46)j¯ + (61° + 15) k, Osts1 Arc Length is equal to

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

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: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 7(x^2) +…

A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

Q: Find the open interval(s) on which the curve given by the vectorvalued function r( ) = 2 cos3 i + 3…

A: Consider the given vector-valued function: Here the objective is to find the open intervals on…

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

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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: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

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 vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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Q: At time to, a moving particle has the velocity vector v = 7i and the acceleration vector a = 7i +…

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Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

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

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Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Find the acceleration vector for the position vector 7 (t) = (sin(11t), 3t', e -*). x component = y…

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Q: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

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

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Q: Let C be the upper half of the circle whose equation is x2 + (y - 2)2 that is generated by revolving…

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Q: Find a vector parametrization of the circle of radius 3 in the xy-plane, centered at (4, -1),…

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Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

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Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (5,…

A: Given: y=x2 at the point (5,25)

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

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: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

A: To find a vector tangent to the curve of intersection of two cylinders        x2+y2=2 and…

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

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Q: 7.) rCt) = (5+,3cot), 3sind), 7.1-> Find the arc length of the curve. 72-) Find the unit tangent and…

A: as per our company guidelines we are supposed to answer ?️only first 3️⃣ sub-parts. Kindly repost…

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: Find a unit vector n that is normal to the surface 4z? – 2x* – y = 18 at P = (1,2,3) that points in…

A: Solution of question is written in below steps.

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: The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by

A: The variables of the spherical coordinate system r,θ,ϕ are given as.…

Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: Q1) Find equation of plane normal to vector 3i + 2j – k and pass through point (1,1,5).

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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: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

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Q: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…

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

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