Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3, 0).

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: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

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Q: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = 1/θ and dθ/dt = t2

A: Given Data The position vector is r=1/θ. The change in angle vector is dθ/dt=t2=2t.   Integrate the…

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: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= 5e a0 and = 1 dt v-Du, +Duo

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Q: Find a unit vector n that is normal to the surface 4z? – 2x* – 3y = 14 at P = (1,2, 4) that points…

A: To Determine: Find the unit normal n that is normal to the surface at p(1,2,4) that points in the…

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: The divergence of the vector F = a²yî + æyz} – a*y°k is x2 y? k is -

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Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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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: Q3/A- Show that for any position vector r the binomai vector B is always orthogonal to the…

A: We have to solve given problems:

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

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

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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: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

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Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Graph the vector field F(x, y)=(-3y, 2x); also find the divergence and the rotational.

A: The graph of the  vector field F=-3y, 2x is as follows

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: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

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: 2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is (In(r² +…

A: Solution-

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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

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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 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: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

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Q: Find the dircctional deriu atrue Du f(-3,-1,3) for the function f Cxiy,2) =xy + yz +ZX in the…

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Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: A body is spiraling upward due to rapidly rising air on a path similar to that of a helix and having…

A: Consider the position vector.

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

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

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Q: A force of (2i - j+k) Newtons acts on a line through point P having coordinates (0, 3, 1) metres.…

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Q: Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at…

A: Consider the given function as fx,y=ln1+xy

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: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

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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: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

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

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