16. Calculate ]] (V × F) · în dS, where F = (y, −x, e²²) and S is the part of paraboloid z = 3x² + 3y², 0≤ z ≤ 6, oriented downward. a. -2π b. -4T c. 0 d. 2π е. 4T

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

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Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: ) Determine the Cartesian Equation perpendicular to the line L1: 4t – 2y = 8, -3t = 6 – 2x with a…

A: Write L1 in Cartesian form. Then find its slope or gradient then use it to find the slope of the…

Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

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Q: EXERCISE 4.4 Given P₁ = (-1, −1, 0) and P₂ = (1, −1, 0), derive the parametric expression (P(u, 0))…

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Q: The value of . (x² +y²) dS, where S is the surface of the paraboloid z = 2- (x² + y2 ) above the x-y…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

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Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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Q: Evaluate v (x? v + x y z²) · dr where C is the line segment from (1, – 1,0) to (2,1,3) | Select one:…

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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: (a) Evaluate APA: – 6) R where R is the solid hemisphere r² + y² + :² – 2r + 4y = 4, : 0.

A: We want to evaluate  ∫∫∫R9-z2dV where R is the solid hemisphere x2+y2+z2-2x+4y=4, z≥0 We can write…

Q: V=R Prooflthat Nisavectors sPoe

A: Given that V = ℝ+ Operations + and · defined as, x + y = xy rx = xr, where x,y ∈V; r ∈F To prove: V…

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: Use Cartesian coordinates to evaluate JIJ y² dv D where D is the tetrahedron in the first octant…

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Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

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Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,– 1)? A. x =…

A: We know that parametrization of the line connecting pointsx1,y1,z1,x2,y2,z2 is given by x=x1+tx2-x1;…

Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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Q: Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point…

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