Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes of an orthorhombic lattice with the ratio of the axial lengths as: A: B: C 2: 3:2

Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

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Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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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: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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Q: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

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Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

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Q: Given F(x, y, z) = -yzi + xzj – xyzk be a vector function that passes through a surface S of z + x2…

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Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: In the (yz) plane consider the polygon A of vertices (5, 0) (8, 1) (11,0) and (8, – 1) The volume of…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

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Q: Use triple scalar product of (u*v)*w to find the volume of the parallelepiped having edges…

A: The given vectors are u = i + j + k v = 9i + 3j +2k w = 8i + 10j + 5k

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges: u = i…

A: We have to find the volume of parallelepiped used the scalar triple product.…

Q: Use the figure at the right for Exercises 8-11. 8. What are two other ways to name EF? 9. What are…

A: In the question we need to name line and plane.

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Find the volume of parallelepiped

Q: Compute the orthogonal projection of point A H coordinates (2,0) onto the Set M (the closed unit…

A: Hint: The formula of orthogonal projection of a point w on a set Aa1,a2,a3,... is…

Q: Find the perpen dicular trajec ories of the plane faimily its intersection X -y +2 = Ł Cヒ cons tan+)…

A: Given surface is x -y +z = k  --- (1)                          ⇒z = k -x+y The parametric equation…

Q: Which of the following planes is parallel to the plane 3x – 2y + z= 3? - Oz=3x- 2y + 9 z = 6x- 4y +…

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Q: A tessellation is a collection of two-dimensional figures that fit together to cover a plane or part…

A: True

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Show that the tangent plane to the quadric surface at the point (x0, y0, z0) can be written in the…

A: Given surface is x2a2+y2b2+z2c2=1 To find the equation of the plane, find the normal of the given…

Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +…

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1…

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c.…

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0

Q: Let C be the cubic region delimited by the coordinate planes and by the planes x = 2 y=2 and z=2 in…

A: the planes x = 2 y=2 and z=2 in the first octant.

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: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Let S be the sphere of radius 1 centered at (2, 3, 4). Find the distance from S to the plane x + y +…

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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: The barycentric coordinates of a point P with respect to the non-collinear points A, B,C is given by…

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Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D…

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Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Prove that the shape ABCD is a rhombus. With A(1, 4), B(3, 0), C(1. -4) and D(-1,0).

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

A: Solution :-

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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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: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: In R, let S be the piece of the plane 3x + 3y + 3z = 3 that lies in the first octant, oriented…

A: Given S is the piece of the plane 3x+3y+3z=3 that lies in the first octant oriented upward. The…

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 2,0), (0, 0, 5) and the origin. Writel II|…

A: Follow the steps to find the upper limit of x and z to solve the problem.

Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 3i…

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Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

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: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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Q: Find a Find a funds on the surdace 7=372y8 at which the feugend Planes is Parallel to the Plane…

A: We have to find the value of points on the surface

Q: 1 %3D 12 27

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