For X = (x₁,...,xn), Y = (y₁, ..., Yn) € Rn, define n d(X,Y) := Σ |xi - vi| i=1 (a). Show that d is a metric on R". (b). Let de be the Euclidean metric on Rn. Find positive real numbers a, ß such that adE (X, Y) ≤d(X, Y) ≤ BdE (X, Y)

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A: As per rule I need to solve only first three subparts.

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A: Solution:

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A: Please see the below picture for detailed solution.

Q: Consider the following mappings on RXR: * d1(x,y) = ex-y, d2(x,y) = |2x -y and d3(x,y) = √√x - yl O…

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A: Suppose we have  Then we have to answer the following...

Q: Consider the following mappings on RXR: d1(x,y) = e*-Y, d2(x,y) = |2x –yl and d3(x,y) V=yl O Both d1…

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Q: 86. The unit nomal vecter to the curwe x?+y2 + Z² = 4 at (1,1,1) is %3D fa) li+aj+k)NI fb) lit2j+k)…

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A: Given , f(x,y,z) = (30-x , z+22 , y)

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A: Let  for all Let the point be We need to calculate the tangent and normal spaces to C at p.

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A: Curl F ( -1, y-z ,1-z)

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Q: d1(x,y) = e*-y, d2(x,y)= |2x – yl and d3(x,y) = /]x – yl %3D %3D O Both d1 and d2 are metrics on R.…

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Q: Question 3 Consider M = R² with the metric di(u, v) = |x-a|+|y-b for u = (x, y) = R², v = (a, b) =…

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