Let C be the curve with vector function 7(t) = (cos(vt), sin( Vt ), /3t ) for 0sts“,. 4 a) The linear mass density, in kg/m, at each point of a wire in the shape of Cis given (numerically) by the square of the distance from the point to the origin. Find the total mass of the wire C. (Units on the coordinate axes are meters.) 1 b) Consider the force field defined by F(x,y,z)=( xy, x, with components measured in Newtons. Find Z 37 the work done by F as a particle moves along C. Notes: You do not need to include a sketch of this curve. Start each integral calculation with a clear statement of general integral form.

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Q: H.W. Find the unit normal vector to the curve at t=2, r(t) = 4t i-3 t j.

A: Unit normal vector is N(t)=T'(t)‖T'(t)‖ here T(t) is unit tangent vector and T(t)=r'(t)‖r'(t)‖ So we…

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A: The complete solutions are given below

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Q: Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is…

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A: please comment if you need any clarification. If you find my answer useful please put thumbs…

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Q: Find the work done by a force of 14i (newtons) in moving as object along a line from the origin to…

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Q: Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is…

A: Solution is uploaded below

Q: Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.