4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

Q: 36 Find the equation of the tangunt Hne plane at l'2,1) and f L1.95, to fxiy) = Jao-xa - Tya %3D use…

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Q: D

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Q: 7. In AVYX, the centroid is Z. Use the diagram to solve the problems. If VP = 51, find VZ and ZP.

A: We use the property ,the centroid divides each medians in the ratio 2:1.

Q: 2 Consider the line L: y -1 +t|0, te R, and the plane T : x – 4y – z = 6. (a) Show that L is…

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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: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

Q: 25. Evaluate F.N dS where F= yl + 2xj –- zk and S is the surface of the plane 2x +ye 6 in the first…

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Q: 2. Show that the xy plane W = (x, y,0) in Rº is generated by: (i)u = and v = (ii)u : and v = 3

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Q: 5 3 - 2 Let y = 1 Find the distance from y to the plane in R° spanned by u, and uz. -2

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Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: 8. Let S be the surface {(x, y, 2) | a = y? + 22 + 1}. Find every point (ro, yo, zo) on S so that…

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Q: 4. In a rhombus WXYZ, WXY = 108°. Find () XY, (ii) XỸZ, (iii) XÂWY. %3D

A: Answer: Given W X^ Y =108° →(1) In a rhombus the diagonals bisect the angle at the vertices→(2) The…

Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp&lt;0.…

Q: Use Green's theorem to evaluate $(xy + 3x²)dx + (3y – 2x)dy, along C, where Cis the triangle with…

A: Given Integral ∮(xy+3x2)dx +(3y-2x)dy along c where c is the triangle with vertices (0, 0), (0, 3)…

Q: 9. What is the xy trace of the sphere (x – 5)2 + (y – 2)² + (z – 10)² = 16 ? а. (х — 5)2 + (у — 2)2…

A: To find the xy trace of sphere, put z=0 in equation of sphere.

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: 2. Bounded by the paraboloid = 10 – 322 – 3y? and the plane z = 4 (using polar coordinates)

A: The paraboloid is bounded by z=10-3x2-3y2 . Now, converting in polar coordinates, z=10-3r2.

Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: In ANPQ, U is the centroid. If NS=15 find US. R S U

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Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

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Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: 59. Find all points on the portion of the plane x+y+z35 in the first octant at which f(x, y, z) = xy…

A: We have to find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y,…

Q: 2 The values of a and b such that the surfaces ax - byz = (a + 2)x and 4x2y + z3 = 4 cut…

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Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

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Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x +y that lies above the…

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Q: Let C denote the triangle with vertices at (0, 0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: We have to apply the green's theorem here.

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: 2. Show that the xy plane W = (x, y, 0) in R³ is generated by: (i)u = 2 and v= |1| (ii)u and v = 3…

A: Given the plane: W=(x,y,0) in ℝ3.Let (x,y,0) be any element from W. For a and b in ℝ, we…

Q: 3.4.8 Show that the sphere x² + y² + z² = 1, z ≥ 0. JJ,z²dS=, where S is the surface of

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: Consider 2-dimensional hyperbolic space with metric ds = dr'+dy and y > 0. The length of a line…

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Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

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Q: 3.4.6 Use Green's theorem in a plane to evaluate of 10x9²³- [(xy²-y) dx + (x + y²) dy] C as a double…

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Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: 4. Suppose that VxF= (0,1,-1), S is the plane x + y + z = 1 in the first octant and Cis the boundary…

A: Given: ∇×F=01-1 S is the plane x+y+z=1 in the first octane  and C is the boundary of S. Now, to find…

Q: 7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3,…

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Q: 15.4.10. ſſy(x + y + z) do, M is the surface x? + y² + z² = 4, z > 0.

A: We need to find surface integral.

Q: 7. D is bounded by the surface (a2 + y² + z²)² = a²(x² + y? – z²). %3D

A: Sol

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…