1.Find the area of the surface. a. The part of the plane 2x + 5y + z = 10 that lies inside the cylinder x² + y? = 9 b. The part of the surface z = 1+3x + 2y? that lies above the triangle with %3D vertices (0,0), (0, 1), (2, 1) c. The part of the paraboloid z = 4 – x2 – y² that lies above the xy- plane |

Q: 3. Let OÁ = i +2j+ k, OB = 3i+j+2k and OC = 5i+j+ 3k. (a) i. Find AB × AČ. ii. Find the area of…

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Q: I3D Find the coordinates of the point (x, y, z) on the plane z = 2 x + 2y + 2 whi X = y =

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Q: Find the area of the surface. The part of the plane z = 5 + 5x + 2y that lies above the rectangle…

A: given  z = 5 + 5x + 2y               ⇒  ∂z∂x = 5   and  ∂z∂y = 2                  ds =…

Q: Find a parametric representation for the surface. The part of the hyperboloid 3x² - 3y²z² = 3 that…

A: Introduction: The coordinates of the points that make up a geometric object, such as a curve or…

Q: Find a parametric representation for the surface. The part of the hyperboloid 2x2 − 2y2 − z2 = 2…

A: We have to find paramatric representation of the hyperboloid 2x2 -2y2 -z2 = 2 by using u and v.

Q: 2. Evaluate ([.(Vx F). ds, where S is the surface of the paraboloid x2 + y2 + z = 4 above the…

A: We have given F→=(x2+y-4)i+3xyj+(2xz+z2)ksurface is given x2+y2+z=4 and above the xy planediagram of…

Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find the point on the sphere x² + (y + 2)² + (z+ 9)² = 4 nearest to a. the xy-plane. b. the point…

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x² +y that lies above the…

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Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the…

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