Calculate F. dS where F = (4r*z, 4y°z, 324) and S is the surface of the solid bounded by the hemispheres z = 16 – a² – y², z 4 – a? – y? - and the plane z = 0.

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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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: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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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: . Consider the plane P : x +y + z = 2 and point A(0,1, 2). A line L has the parametric equations L:…

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Q: Let L be the line with parametric equations x = 2+t, y = 5-2t, z = 4 + 3t. Let S be the plane that…

A: Given L is the line with parametric equations x = 2 + t , y = 5-2t , z = 4 + 3t . Let S be the plane…

Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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

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Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: equation of the line. -y+22-0 passing through cting line e:x=2+t,y=st,

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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: 1. Find the distance from the point S(2,–3,4) to the plane x + 2y+ 2z = 13 2. Find the distance from…

A: 1. Point : S2,-3,4   Plane : x+2y+2z=13   2. Point : S0,-1,0   Plane : 2x+y+2z=13

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: The tangent plane equation of the level surface z =-x² – 3y² at point (2,2,-16) is. O a.…

A: Given: The tangent plane equation of the level surface z=-x2-3y2 at point (2,2,16)

Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…