find the unit vector normal to the surface.

Q: 2. Find T, N the unit bi-normal vector B, and k at the given t value. (2b) r(t) = ( cost, sint, In…

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Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

Q: z?i + x²j + y²k, find the curl of F and the component of curlF along the tangent vector to the curve…

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Q: EXERCISES 5: Find equations for the (a) tangent plane and (b) normal line at the point Po on the…

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Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder + (y − 1)² = 1 (a)…

A: We will use the basic knowledge of vector calculus and differential calculus to answer all three…

Q: 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2,…

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Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

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Q: 1. Find the unit tangent vector T(t) and principal normal vector N(t) for the curve r(t) = (2…

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Q: 5) Consider the surface S shown in the graph, whose parametrization is given by by: r(u, v) = (v²,…

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Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).

A: Please check step 2 for the solution.

Q: (i) Compute r(1) and r'(1). (ii) Find a parametric equation of the tangent line to r(t) at t = 1.…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) 12x…

A: Given equation of the surface  xyz=12 Point on the surface is 1,3,4 (a) Find equation of tangent…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

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Q: Reparametrize the curve with respect to arc length measured from the point where t = 0 in the…

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Q: Find an equation of the tangent plane to the surface at the given point 1, 1 4 z arctan X Find…

A: To work out the required equations using partial derivatives

Q: Q3/ find equations for the (a) tangent plane and (b) normal line at the point Po on the given…

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Q: Consider the surface s shawn in the figure with the following parameters. r(u,v) = (ucosv, usin v,…

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Q: Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢<a /3, 1<z<2 Н-Iz /2пр…

A: according to stokes theroem closed linr integral of H is same as the surface integral of curl of H.…

Q: Consider the ellipsoid 3x? + y? + z² = 11. The equation of the tangent plane to this ellipsoid at…

A: 3 x2 + y2+z2=11 and the point is (1,-2,-2)

Q: (d) Use Stokes' theorem to evaluate S. F.dr where = z²î + y²j + xk and C is the triangle with…

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Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0&lt;=t &lt;= pai.

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 8, (1, 2, 4) (b)…

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Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Find and equation of a) the tangent plane and b) the normal line to the given surface at the…

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Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface x*…

A: According to bartleby guidelines when student asks more than one question expert have to answer…

Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

Q: Find the equations of (i) the tangent plane and (ii) the normal line to the surface z = excos(y) at…

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Q: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 4, 3) %3D…

A: Apologies for the inconvenience.   #b) In part #a) we have found that, the direction ratio of the…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 4, 3) 12x…

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Q: 2. Let z = f(x,y) = x³ + xe* +y?. (a) Find an equation of the tangent plane to the surface z = f(r,…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: H-pz cos At point (1, x/3, 0), find (a) H a, (b) HX & (c) The vector component of H normal to…

A: As per bartleby guideline for more than three sub parts asked only first three are to be answered…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the fur 5x…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A: Given that  The equation  cos(πx)-x^2y+e^(xx)+yz=4  Point (0,1,2) To find the equation of the…

Q: Consider the function f(x, y) = x³+2xy+y. (a) Give the linearization L(x, y) of f at (2,3). (b) Use…

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Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: O Solve the electric flux through a paraboloid z =x² + y² – 16 that lies below plane z = 0. It is…

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Q: Find a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: 7. The magnitude of the normal vector t, xt for a sphere of radius a in parametric form where u = p…

A: Radius of the sphere is a. It is given that,u=ϕv=θ In parametric form, the sphere can be represented…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: Here we use the concept of gradient of a scalar function at given point.

Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

A: Given F→(x,y) = -ysin(x)i→+cos(x)j→ a) Let us assume x=t then y=x2=t2 by differentiating r→(t) with…

Q: )) Check whether V (x, y) = Ce-kxsin(ky) is a solution to the two-dimensional Laplace's equation.…

A: For the solution of the problem follow the next step.

Q: #2. Find an equation of the tangent plane to the given parametric surface at the given point (a) x =…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: Find a vector normal to the surface x2 + y2 − z = 0 at the point (3, 4, 25). Find the equations of…

A: Given: The equation of the surface x2+y2-z=0 at the point (3,4,25)

Q: (d) Use Stokes' theorem to evaluate f. F.dr where F = z?î + y²j + xk and C is the triangle with…

A: Stokes theorem is used to evaluate integration