(2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

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A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

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A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

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Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t>0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

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Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

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A: Let the 2 points in the line segment be,

Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

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A: At point of intersection both the functions will have the same value therefore f = g

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Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: Compute the length of the curve r(t)= (-5t, 4t – 3, – 5t + 5) over the interval 0 <t< 7

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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A: F(x,y) = y ln(2x + 7y) To find : fx and fy

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: Let C be the curve y = 2/r for 1.3 <x < 3.2.

A: Given that: y=2x

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Q: 2- Find the value of x which make the line containing CO the Points Cx, 5) and (-2,3). Parallel to…

A: Given condition is that both line are parallel , hence slope of both line are equalslope of line(m)…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

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Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

Q: The graph of fo- is concave down on interval (-1,1) A (0,1) B (-0,0)U(2,00) .C (-x,-1)U(1,00) .D

A: The intervals where f(x) is concave down, the tangents drawn on the curve lie above the curve.

Q: graph the points z = x + iy that satisfy the given conditions. 5. a. |z | = 2 6. | z - 1| = 2 7. |z…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

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Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

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Q: Find the set of points that is satisfied the condition described by |z – 2i|+ |z + 4i| = 10

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Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

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Q: Is AX'Y'Z' a reflection of AXYZ across line g? g X. Z' Y X'

A: