Question No o4 cylindrical Coordinater ·are Show that grad (log 8) and grad o are solenoidal vectors

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 82 In the overhead view of Fig. 5-65, five forces pull on a box of mass m = 4.0 kg. The force magni-…

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Q: (a) Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin(x) at the…

A: Given: y=8sinx and the point π6,4.

Q: 4. If p, 0, z are cylindrical coordinates, show that grad (log p) and grad o are solenoidal vectors.

A: In cyclindrical coordinate systemx=p Cosϕ , y=p Sinϕ , z=zP≥0 , 0≤ϕ<2π , -∞<z<∞dx=dp Cosϕ -…

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Q: Ps Fnd Parametric equations for the 3. lines through (2,3,0) Perpendliculerr to the Vector uiitzj+3k…

A: First take cross product ie normal vector And then use formula

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Q: 2. A box weighing 135 N is resting on a ramp that is inclined at an angle of 25°. Resolve the weight…

A: Find your answer below

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Q: 2.4 A unit normal vector to the cone 30° is: (a) a, (c) a (b) ag (d) none of these

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Q: Question 10 The r in cylindrical coordinates must be positive or zero. O True O False

A: Given - "The r in cylindrical coordinates must be positive or zero."

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Q: find The unit Vectors tangent and normal toThe ellipse x+ 2y=6 6at The Point (2,1).

A: I am going to solve the give problem by using some simple geometry to get the reuired result.

Q: 2/63 A partícale which moves in two-dinensional إحراثیاته' - حركه با لبوصة motion has Coordinates…

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Q: For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||2||b||? – (a · b)? ах

A: Use the vector product and scaler product identity, a×b=absinθn^…

Q: 7. For vectors a and b in R? prove Lagrange's identity: ||a x b|? = ||a|| ||b||? – (a · b)?

A: for vectors a and b in ℝ2 prove -lagrange's identity a×b2=a2b2-a·b2

Q: The figure shows an overhead view of a 0.026 kg lemon half and two of the three horizontal forces…

A: Given that, F1 = 3N at θ1=31° F2=10N at θ2=33° (a) If the lemon half is stationary, then Fnet = 0.…

Q: The figure shows an overhead view of a 0.026 kg lemon half and two of the three horizontal forces…

A: Given that, .m=0.026 kg, F1=3 N, θ1=31°, F2=10 N, θ2=33° obtain the force vector for the given…

Q: - I he symmetrie equidton of alne quation of alme Find the paramedic equation

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

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Q: 10 Give an expression of a vector, B = aR + R cosoae + a, in Cartesian and R cylindrical…

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Q: Find an expression for a unit vector normal to the surface x = 8 cos (0) sin (4),y = 5 sin (0) sin…

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Q: Express the following vectors in Cartesian coordinates and spherical coordinates 1- A = pz sin p a,…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: A communications satellite moves in a circular orbit around Earth at a distance of 42,000 kilometers…

A: (a) Since the orbit is circular. Let r→=rcosθi^+r sin θj^. Differentiate the equation with respect…

Q: Prove V," - n(n+1)r"-² wheren is a constant.

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Q: 7. For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||*||b|² – (a - b)²

A: Let's find.

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: