where S = [0, 1]; Q3: (a) In the metric space (S,d), vx, y es. If A = [0,2), then find the following: A; A d(x,y) = [x-yl: A' ; A.

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Q: Evaluate F.dr where F(x, y)-ny I+ej and Cis the line segment from (2. 0) to (4, 0). a) 0 b) 2 c) - 2…

A: Solved below...

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A: Given, x,y ∈ R2 To show: p=x.yy.yy is the closest point on the line span y to x

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Q: P.(98) Q 10. Show that Rº= span (1²³] 11]).

A:

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A: Given: point 3,-1,4 and equation of line x=4-t, y=3+2t, z=-5+3t Formula: The distance between point…

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Q: 5. What is the distance between points N and M? y K L (0,3,-3) M ++ P (0,0,-3) Q (0,0,0)

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Q: The height (feet) of a balllaunchedin the aur (t) Seconds after it is launched is giuen by. flt)=…

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Q: 1, Compute the Euclidean distance between the sets of points below. a. ​(2​,4​)and ​(9​,3​) b.…

A: a) two point in 2 dimension is (2, 4) and (9, 3)  b) two point in 3 dimension is (11, -3, 30) and…

Q: Given z1, z2 E C, define the distance between z1 and z2 by setting: d(z1, z2) := |21 – 22| . Prove…

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Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: F. Let a = :(a1, a2, ..., an) E R" where ||a|| +0 and let be R. Let SC R" where S = {(x1, x2, ..,…

A: Given- Let a = a1, a2, ⋯, an ∈ ℝn where a ≠ 0 and let b ∈ ℝ. Let S ⊂ ℝn where S = x1, x2, ⋯, xn ∈ ℝn…