The coordinates of the AB part of the homogeneous wire in the x, y and z axes

Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. (x + 2)2 + y2 + (z - 2)2…

A: To determine the centre and radius of the sphere.

Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

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Q: Consider the parallelepiped with adjacent edges u = 4i + 3j + k v = i+j+ 4k w = i+ 9j+ 2k Find the…

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Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. x2 + y2 + z2 - 6y + 8z =…

A: We’ll answer the 51th question since we answer only one question at a time. Please submit a new…

Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

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Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: Exercise 16.6.12. Given (0,0,0), Ji (1,2, 3), T2 (6, 5, 9), Üz = (4,8, 2), write down the Cartesian…

A: The barycentric coordinates of the cartesian coordinates x1,x2,x3 is 1-x1-x2-x3,x2,x3 The first…

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

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

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k, v…

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Q: 14. Find the volume of the parallelepiped having i + 3j + 2k, 2i + j- k and i- 2j + k be the edges.…

A: The edges of the parallelopiped is given to be a=i+3j+2k, b=2i+j-k, c=i-2j+k. To find the volume.…

Q: Consider the parallelepiped with adjacent edges u = 5i + 9j + k v = i+j+3k w = i+ 5j + 7k Find the…

A: volume of the parallelepiped is given by  u→·v→×w→

Q: Z is the centroid of AUVW. What is UY if UZ = 8? O A. 4 о с. 6

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Q: Find the area of the surface. The part of the paraboloid r(u, v) = ucosvi+usinvj+u*k; 0<us3,0svS2n 5…

A: Area of the surface is given by:          A=∬ru×rvdudv

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Given data: *The vertices of the triangle is (2,2), (2,7) and (4,7) From the coordinates of the…

Q: Among all rectangular solids defined by the inequalities 0sxsa, Osysb, 0szs 1, find the one for…

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Q: M 13. Are points J, K, and L collinear? 14. Are points J, K, and L coplanar? 15. Are points J, K,…

A: Since you have asked multiple question, we will solve the first 3.question for you as per our guide…

Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤ b, 0≤z≤ 1, find the one for…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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Q: 4) Name a point that is coplanar with A, B, and C. b. E D a. D d. N C. F 3)

A: the given figure we have to name a point that is coplanar with A, B and C.

Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: . Consider a two-link planar robot ori- ented in the elbow-down position as shown in Fig. P3.26. If…

A: In this two-link planar robot oriented in the elbow down position, x=-1,y=15,l1=10,l2=8 The formula…

Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

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: In the (yz) plane consider the polygon A of vertices (3,0) (4, 2) (5, 0) and (4,-2) The volume of…

A: The volume of the solid of the revolution can be calculated using Pappu's theorem. The formula for…

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: 12- Evaluate JJI (x2 + y? + z?)dvwhere B is a ball with center the origin and radius 5. B

A: Given problem is :

Q: =7. Consider a two-link planar robot, with positive orientations of 0, and 0, as shown in Fig.…

A: Solution :-

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤b, 0≤z≤ 1, find the one for…

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Q: (b) Evaluate SSI, zdV, where D is the solid tetrahedron bounded by the four planes x = 0, y = 0,z =…

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Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Convert the following point from cylindrical to rectangular coordinates: (* ). 11a 6, (x, Y, z) =…

A: The given point in cylindrical coordinates are   6,11π6,9. We know that if cylindrical coordinates…

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the…

A: To find- Evaluate ∭Ez dV where E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 in…

Q: Pr. #1) || zdA, Dis the triangular region with vertices (0,0), (4, 2), and (0,6) (aketch D on the…

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Q: Among all rectangular solids defined by the inequalities 0≤x≤ a, 0sysb, 0szs1, find the one for…

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Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Using washer method

Q: 5. USC cyllndrical coordinates. Evaluatc (k4)dv, where E IS the solid that ies betwern the cylinders…

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Q: Consider the solid in xyz-space, which contains all points (x, y, z) whose z-coordinate satisfies 0…

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Q: Let B be the ball with center at the origin and radius 1 SSS 4(2² + y² + z?)dV = O 24 5. 127 16

A: We will evaluate the given integral.

Q: Let T be the tetrahedron with vertices (5, 0, 0), (0, 2, 0), (0, 0, 5) and the origin. Write II|…

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

Q: 15. The solid enclosed by the sphere x2+ y2 + z2 = 4a? and the planes z = 0 and z = a. %3D

A: Given: x2+y2+z2=4a2          ... (1) z=0z=a

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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

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Q: In cylindrical coordinates, the set {(r, 0, z): 0<r< 1, 0<0 <T, -1 <z < 1} is (a) a full right…

A: In the given cylindrical coordinates, r,θ,z Radius of the cylinder lies between 0 to 1. r=0≤r≤1r=1…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.