3.Compute ((x + y)² + z² + 2yz)dS, where Σ is the sphere f x² + y² + z² = 2x + 2z.

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: Write the sphere equationil odi lo anoitaupo ontemeeg bas Totoov bnif (d) x2 + y? + z2 + 2x - 4y –…

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: If x² + y² +2²-12x+4y+15= 0 is a sphere with center (2o, 3o, 2o) and radius r, what is r (o+yo+zo) ?…

A: The given sphere has the equation      x2 + y2 + z2 - 12x + 4y + 15 = 0    =&gt; (x2 - 12x + 36) +…

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

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: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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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: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: π be the plane that touches the sphere E with center C= (2,2,2) at the point A=(7,4,2).The line…

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Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

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