(a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F = xi+yĩ + zk. (b) Check your result using the divergence theorem.

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

A:

Q: c) The surface S is the portion of the plane x+y+z=1 in the first quadrant of the Oxyz Cartesian…

A: Given: The surface and curve is shown below   The region s is the triangle and the curve C is the…

Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

A:

Q: 8.) Find the planes tangent to the following surfaces indicated points: a:) x² + 2y ²2/3 X ² = 10₁…

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Q: classify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)

A: Here we have given a surface equation as below:  x2+2y2+z2-4x+4y-2z+3=0 The surface given by the…

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: Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .

A:

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: 2. Consider the line r(t) = (4t+1,3, 2 - t) and the ellipsoid + + z? = 1. What is the distance from…

A: Consider the line  and the ellipsoid To find  distance from the point (-3,3,3) on the line to the…

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

A:

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below