A tessellation is a collection of two-dimensional figures that fit together to cover a plane or part of a plane with no overlaps and no gaps. True O False

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: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

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Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

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Q: In the three-dimensional space, consider a cube Q and a plane P passing through 4 vertices of the…

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Q: Answer True or False z = 5 is a plane in space. Select one:

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Q: A plane in 3D-space system A. is generated by at least three points. B. can lie in more than one…

A: A plane in 3D-space system is generated by three points from which if the first nd second points…

Q: can tessellate a plane. O Regular octagon O Regular heptagon O Equilateral triangle O Regular…

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Q: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: (True/False) Two lines in three-dimensional space parallel to a plane are parallel to one another.

A: Given that  Is two lines in three dimensional space parallel to a plane are parallel to each…

Q: Give a geometric description of the set of points (x, y, z) that lie on the intersection of the…

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Q: 3. Prove that a flat surface of revolution is part of a plane, cone, or cylinder.

A: prove that a flat surface of revolution is part of plane or cone or cylinder. solution a flat…

Q: where P is the parallelogram Spanned by the Vectons 24,13 and <3,3) with tHanformation X=4u+3V and.

A: Given that ∫∫Pe4x-ydxdy where p is the parallelogram spanned by the vectors 4,1 and 3,3 with…

Q: Draw an obtuse triangle and, by construction, find the centroid of the triangle. (HINT: Begin by…

A: To get an obtuse triangle, draw a triangle with one of its interior angle should be greater than…

Q: Describe the intersection of the prism and the plane.

A: Given figure of the rectangular prism is,

Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: Write the intersection of plane UVYZ and plane SVWZ? T.

A: given figure is pointed by vertices S, T, U, V, W, X, Y, Z

Q: Calculate the volume of the parallelepiped spanned by u = (2, 2, 1), v = (1,0, 3), w = (0, -4, 0)

A: u→=&lt;2,2,1&gt;v→=&lt;1,0,3&gt;w→=&lt;0,-4,0&gt;Volume of…

Q: Find the volume of a parallelepiped spanned by 2i - 5j - 7k, i-k and 9i – 3k.

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Q: Give a geometric description of the set of points (x, y, z) that lie on the intersection of the…

A: Given Data The equation of a sphere is x2+y2+z2=5. The value at z-axis is z=1.   Put the values in…

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

A: To calculate Miller indices we have to take reciprocal of ratio of intercepts and axial length

Q: A postulate states that any three noncollinear points e in one plane. Using the figure to the right,…

A: The objective is to find the plane that contains the points Z, S, and Y and then determines whether…

Q: Find the volume of a parallelepiped whose edges are ä = 7i+5j-k, 6-j+4k and e= 4i-3j+6k %3D

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Q: Consider the parullelepiped with Sider. t-Findthe Volume of the Paralletefiped 2 Findthe…

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Q: Determine whether the statement " Two planes in space are either intersecting or parallel ", is true…

A: The given statement is ''Two planes in space are either intersecting or parallel''.

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Which of the shapes below can make a regular tessellation of the plane?

A: there are only three regular polygons for tessellation and they are equilateral triangle, square and…

Q: What cross-section cannot be formed by intersecting a plane with a right cylinder? Campbol OM…

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Q: A surface is called bounded if there exists M &gt; 0 such that everypoint on the surface lies at a…

A: Explanation: The possible Quadric surfaces are Spheres, Ellipsoids, Hyperboloid of one sheet,…

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: A cube with a cylinder cut from Its center is cut along the plane shown below. Which of the…

A: When the cube with a cylinder cut from its center is cut along the plane as shown in the figure,

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Describe the intersection of the horizontal plane z = h and thehyperboloid −x 2− 4y 2 + 4z 2 = 1.…

A: Put z=h in given equation -x2-4y2+4h2=1⇒x2+4y2-4h2=-1

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: Let C be an ellipse in a horizonal plane lying above the xy-plane. Which type of quadric surface is…

A: Given, Let C be an ellipse in a horizontal plane lying above the xy-plane.

Q: You are given the following points: A = (-4, 20, 16), B = (20, 0, 7), C = (8, –15, – 19). %3D Which…

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

Q: Find the volume of the parallelepiped spanned by u = (1, 0, 4), v = (1, 2, 1) and w = (-4, 2, 9) in…

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Q: Find the equations of planes passing through point (a,0,0) if these planes intersect one-sheet…

A: As per the question we have to find the plane which is tangential to the surface of the hyperboloid…

Q: Make a sketch of two parallel planes intersected by a third plane that is not parallel to the first…

A: To draw the sketch of two parallel planes intersected by a third plane that is not parallel to the…

Q: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

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Q: Surface o is a plane a +y + z = 1 that lies in the first octant. Evaluate

A: Given, surface σ is a plane x+y+z=1 that lies in the first octant. To find              ∬σ(2x+z)dS=…

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: can tessellate a plane. O Regular octagon O Regular decagon O Regular hexagon O Regular heptagon

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Q: ) List the four rigid motions on the plane b) What are the three regular tessellations (tilings)of…

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Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: Show that the two planer diagram represent the homeomorphic surfaces

A: Given:-                 Show that the two planer diagram represent the homeomorphic surfaces

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.