Let r be the separation vector from a fixed point (x′, y′, z′) to the point (x, y, z), and let r be its length. Show that: (a) ∇(r2) = 2r (b) ∇(1/r) = −(r-hat)/(r2) (c) What is the general formula for ∇(rn)?

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A: The detailed solution of the problem is given in the next steps.

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A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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A: To find  is the unit vector parallel to .

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A:

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A: R→=xi→+yj→+zk→ and r=R→, a constant vector A→=a1i→+a2j→+a3k→

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A:

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A:

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A:

Q: Consider the R − R 2 function r defined by r (t) = ￾ t, t2
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A: This is a problem of vector calculus.

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A: Given that, gu,v=u2e-v,8,0 and v=3i+4j. Find the value of ∂g∂u and ∂g∂v at the point (8,0).…