(a) Prove that f is a one-to-one correspondence. (b) Prove that ray AF is between rays AB and AE if and only if f(∠BAF) is between 0 and f(∠BAE).

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A: To find the vector projection of vector x onto vector y, we'll use the formula:projy​(x)=(x⋅y) /…

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A: Angle between two vectors is given by,

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A:

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A:

Q: Let F=(9xy,7y,8z)=(9xy,7y,8z). The curl of F=( Is there a function f such that F=∇f=∇?  (y/n)

A: The given function .We have to find the .

Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

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Q: Let F (8xy, 3y, 8z). = The curl of F = (000). Is there a function f such that F = V f? ☐ (y/ (y/n)

A: Step 1: Step 2: Step 3: Step 4:

Q: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

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A: Given vector function The length of the path is found by the formula Given interval is 0 to 1

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A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

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Q: Let F = SOFF Use Stokes' Theorem to evaluate . dr, where C is the triangle with vertices (6,0,0),…

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Q: Match the space curves in the figure below with the following vector-valued functions: O A. r(t) =…

A: See that options ,  A )  r ( t ) = &lt; 1 , t , t &gt;  If we consider the first two coordinates ,…

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A: According to our guideline we are supposed to answer only one asked question.kindly repost other…