Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related with it :

Q: Let A(5, -1, -3) and B(1, 3, 2) be two points in R. The directional derivative of f(x, y, z) = xy…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

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 space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

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Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: Consider the vector function r(t)=⟨t,t^2,t^4⟩ Compute r′(t)=⟨  ,  ,  ⟩ T(1)=⟨  ,  ,  ⟩ r′′(t)=⟨  ,…

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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: given the vector function f(t) = (t, e', –2cos 2t) determine a)df/dt f(t)dt

A: The vector function is given by ft = t2, et, -2cos2πt To evaluate: a dfdtb ∫01ftdt

Q: For y'= Aj where A is given below %3D A= find the right hand side vector F(t, ) needed to apply…

A: Given y'→=Ay→ Here A=1245 We have to find right hand side vector F→(t,y)→.

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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

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Q: Find a vector parametrization 7 (t) for the intersection between the two surfaces: x² + 10y4 + 223 =…

A: According to the given information, it is required to find a vector parametrization for the…

Q: Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j, 0<t…

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Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

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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: Let the velocity vector be v(t) = (2 cos(t), 5t“, 12 exp(3t)) and the initial position vector be…

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Q: Find a unit vector normal to the plane containing v=i+3j-2k and w=-2i+j+3k.

A: There are two types of quantities that exist in nature, one is scalar quantity and the other one is…

Q: Find all points of intersection between the vector functionr(t) =⟨t, t2, t3⟩ and the plane defined…

A: Since the vector is contained in the plane, so all the points of the line intersect with the plane.…

Q: di vergen a of the vector funchion v = xi+ 29j+ 32k, is Jhe 2

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Q: Suppose that ∇ƒ(x, y, z) is always parallel to the position vector x i + y j + z k. Show that ƒ(0,…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 2a² + 2y² and…

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Q: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: (a) Find the domain of the vector function r(t) and sketch its range, where r(t) = (v25 – t², 1, vf²…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

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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: Find a vector function, r(t), that represents the curve of intersection of the The cylinder x² + y2…

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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: 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: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

Q: Find the derivo tive of the function flxy)=xy+y2 in the direction of the vector D-j ot the point…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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 a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: . Let 7 - " be the separation vector from a fixed point (a', y', z') to the point (x, y, z). Show…

A: we have,  fixed point x',y',z'=r' and point x,y,z =r  r→-r→'=x-x'i^+y-y'j^+z-z'k^ a…

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

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

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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: 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: 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: Let the velocity vector be v(t) = (4 cos(t), 5t“, 4 exp(2t)) and the initial position vector be r(0)…

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Q: dA If A (u)is a differentiable vector function of u and||A (u) || = 1, prove that is perpendicular…

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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: Evaluate /| F · dS , where F = and S is the helicoid with vector equation S r(u, v) 0<u < 1, 0 <…

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Q: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

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