e|| x°zdS, where S is the part of the plane z = 1+ 4x + 2y above the rectangle [0, 4] x [0, 2] Evaluate

Q: - || e dA, where D is the open disk D = {(x, y) : x² + y² < 4}.

A:

Q: z dv, where E is enclosed by the paraboloid z = x2 + y² and the plane z = 4. Evaluate

A: see 2nd step

Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

A:

Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

A:

Q: F = (x² – y², y² – 2², z² – x²), S is the part of the plane r + y + z = 1 in the first octant.

A:

Q: || x? zdS, where S is the part of the plane z = 1 + 4x + 3y above the S. Evaluate rectangle [0, 3] x…

A:

Q: Evaluate x² zdS, where S is the part of the plane z = 3 + 4x + y above the rectangle [0, 4] × [0,…

A:

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Is v = 2i - 4j + k related in any special way to the plane 2x + y = 5? Give reasons for your answer.

A: Given:

Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: Evaluate (x2 + y? + z)dS, where S is the portion of the plane z = x + 2 that lies inside the…

A:

Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

A:

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

A:

Q: · Let A the area of the triangle ABC is given by ("1, ул), В %3D (x2, Y2), and C = (x3, y3) be…

A:

Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: The Very Hungry Caterpillar munches his way along a path in three- dimensional Euclidean space…

A:

Q: Evaluate x² zdS, where S is the part of the plane z = 2 + 3x + y above the rectangle [0, 2] × [0, 5]

A:

Q: Evaluate I zdS when (S) is the part of the plane 2x – 13z = 0 that lies above the domain D bounded…

A: first we will take the projection of s onto xy-plane then calculate the required integral using the…

Q: Which of the following is the equation of the plane that is tangent to the surface 2 x2 + y? x z –…

A: Given: 2x2+y2-xz-3z=1

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

A:

Q: Which of the following planes is not parallel to the plane x + y + z = 1?(a) 2x + 2y + 2z = 1 (b) x…

A: x + y + z = 1

Q: 7. Evaluate I = S ads, where S is the part of the plane x+y+z = a lying in the first octant.

A:

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: 286. F(x, y, z) = x²i+ y²j+ z²k, and S is the portion of plane z = y +1 that lies inside cylinder x?…

A: Given, Fx,y,z=x2i^+y2j^+z2k^ for ∬SF.n^ds=∬SFx,y,fx,y.fx,fy,-1 Where z=fx,y=y+1 ⇒fx=0, fy=1 and…

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: Prove that the distance d from a point P (xo, Yo, 2o) to the plane r: Ar + By + Cz + D = 0 is given…

A:

Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: Sketch the following Cartesian Products on the plane R? or in space {(x, y) € R²:x² + y² s 1} ×…

A:

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

A:

Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

Q: Which of the following planes are not parallel to the plane -x+ 3y + z = 3? Select all that apply. O…

A: Our objective is to find the required plane.

Q: Calculate F- dS if F(x, y, z) = x²ye²i+ æy?j – 2xye*k, where S is the surface of the box bounded by…

A:

Q: a) Show that the line I = 0, y =t, :=t where teR a) lies in the plane 6r+4y-4r = 0 b) is parallel to…

A:

Q: // 2° zdS, where S is the part of the plane z = 4+ 2æ + y above the rectangle [0, 5] × [0, 3]…

A:

Q: Let C be any simple closed contour, described in the positive sense in the z plane and write g(2) =…

A: let C be any simple closed contour, described in the positive sense in z plane  gz=∫Cs3+2ss-z3ds…

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

A:

Q: a) Show that the line I = 0, y = t, z =t where te R a) lies in the plane 6z+4y–4x = 0 b) is parallel…

A: In the question it is asked to solve for the planes having equation given below.

Q: Which of the following is the least distance from the origin to the plane 2x + 2y + z = 1? Lütfen…

A: We have to find

Q: Let P be the plane with equation x-2y+2z =-10. Find four distinct points on P at distance 6 v2 to…

A:

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: 17. F = |r|r, where r = xi + yj + z k, S consists of the hemisphere z = /1 – x² – y2 and the disk x?…

A: The solution are next step

Q: Let [] Vị -2 and V2 4 3 k For which value(s) of k will Span{v1, v2} be a plane in R3? A. k= 3 (D.) k…

A: Here, the given vectors are: v1=1-23, v2=-24k Now, the  Span{v1,v2} be a plane in ℝ3 if v1 &amp; v2…

Q: Let P be the plane 2r + u – 7 = 2 and let 0(1.0.3) be a poir

A:

Q: Evaluate | x° zdS, where S is the part of the plane z = 2 + x + 4y above the rectangle S [0, 4] ×…

A: It is given that S is the part of the plane z = 2 + x + 4y above the rectangle [0, 4] * [0, 3]…

Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

A:

Q: Q2) The seraight s line (1,0, 1) +e(2,1,1) intersect The plane X+2y-3#=0 at the point (O,O. D)

A: