6. Let E denote the part of the unit ball above the X-Y plane. Let S denote the surface of E, but only the part below the plane z = V3, F.dS, 2 oriented with the top of S on the outside of E. Compute J₁³ where F(x, y, z) = zy-r y-2x y²+x²

Q: 5. Find a parametric representation for the part of the sphere x + y + z2 = 4 that lies between the…

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Q: Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z =…

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Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Find the surface area of the portion of the plane z=6-3x-3y which lies in the 1st octant I)2sqrt18…

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Q: Let F = 2x3i + 2y3j + 2z3k and let S be the surface consisting of the hemisphere x2 + y2 + z2 = 1, z…

A: Given, F=2x3i+2y3j+2z3k and  S be the surface consisting of the hemisphere x2+y2+z2=1, z≥0 and the…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: 1) let L be the line of intersection of the planes x+y+z=6 and x-y + 2z = 0. Find parametric…

A: To find the parametric equation for the line through the point that is perpendicular to the line of…

Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies 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: 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: arameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.

A: To parameterize the intersection of the plane x = 1 and the surfacez=x2−2x2y+y2, we can set x = 1 in…

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…