Can you find a cross section of a cube that forms a triangle? Explain. Yes, if the plane goes through the diagonal of one face and is perpendicular to the base Yes, if the plane goes through the diagonal of one face and one of the two corners that are not directly below the diagonal. No, any cross section of a cube forms a rectangle No, any cross section of a cube forms a square or a rectangle

Q: Use vectors to find the fourth vertex of a parallelogram, three of whose vertices are (0, 0), (1,…

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Q: Calculate the distance between the point Q(3, 1, 7) and the plane 2x - 6y – z = 3. Don't use a…

A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…

Q: Show that the line of intersection of the planes x +y-z = -12 and 2x + 4y - 3z = -8 is perpendicular…

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Q: Consider the points A(3, – 1, 3), B(4, –3,0), C(-2, –2,0), and D(6, 3, –5). (a) Find the volume of…

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Q: Consider the points A(3, –3, 3), B(4, –5, 1), C(-2, -4, 1), and D(6,3, –5). |(a) Find the volume of…

A: Let's find.

Q: quadrilăteral 1s a purumi 27. In a kite, one diagonal is the perpendicular bisector of other…

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Q: Consider the points A(3, –3, 3), B(4, –5, 0), C(-3, –4, 0), and D(6, 2, –6). Find the volume of the…

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Q: If a plane intersects two parallel planes, then the intersection is OA. a point OB. two…

A: When a plane intersects another plane we get a line.

Q: a) Find an equation of the sphere that is inscribed in the cube that is centered at the point (-7,…

A: (a) To find an equation of the sphere that is inscribed in the cube that is centered at the point…

Q: Points A and B are known to lie in a plane. a. What can you say about AB? b. State the postulate…

A: Solution: Consider the given that A and B are two points in any plane  (a) According to the…

Q: Consider the points A(2, –3, 4), B(4, –5, 1), C(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: Consider the points A(1, –2, 4), B(2, –4, 1), C(-1,–3, 1), and D(3, 1, – 5). (a) Find the volume of…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs…

Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: Consider the points A(3, –3,2), B(4, –5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: Let a, c,d are position vector of point A,B,C,D…

Q: Suppose we know that the points P (0, -1, -1), Q(1, 1, 4), and R (2, -4, 0) form a triangle in…

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Q: Consider the points A(2, –3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: consider the points A(3,-3, 3), B(4, -5,1), C(-2,-4,1), D (6,3,-5) (a) Find the volume of the…

A: We have to find the volume of parallelepiped.

Q: Consider the points A(1, -2,4), B(2, –4, 1), C'(-1, –3, 1), and D(3, 1, –5). (a) Find the volume of…

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, –4, 2), and D(4,1, –8). (a) Find the volume of…

A: The volume of the parallelepiped spanned by vectors a→, b →and c→ is given by a→×b→·c→ We know that…

Q: Consider the points A(3, –3, 3), B(4, –5,0), C(-3,-4,0), and D(6, 2, –6). - (a) Find the volume of…

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Q: In a geometry class, students are asked to describe the dimensions of a plane based on the…

A: In a geometry class, students are asked to describe the dimensions of a plane based on the…

Q: Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). | (a) Find the volume of…

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Q: Consider the points A(1, -2, 4), B(2, –4, 1), C'(-1, –3, 1), and D(3, 1, –5). (a) Find the volume of…

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Q: Consider the points A(1, -2, 4), B(2, -4, 1), C(-1, -3, 1), and D(3, 1, -5). (a) Find the volume of…

A: This is a problem related to vectors. Based on the general formula of volume of parallelepiped we…

Q: Consider the points A(3, –2, 3), B(4, –4, 1), C(-2, –3, 1), and D(5, 3, –4). (a) Find the volume of…

A: Gven points,A3, -2, 3B4, -4, 1C-2, -3, 1D5, 3, -4

Q: (a) Describe the line through P and Q via general (Cartesian) equation(s). (b) Give an equation for…

A: The equation of a line passing through the points x1, y1, z1 and x2 , y2 , z2 can be defined by the…

Q: 29. BUILDING The roof and exterior walls of a house represent intersecting planes. Using the image,…

A: In the given figure, only four planes are shown. The intersecting lines formed from the intersection…

Q: The height of the right pyramid is 25CM and the area of the base is1600CM2 . The intersection area…

A: Detailed solution based on given data show below

Q: Sfor fig shuwn, find the plane using algebric methorde C0,0,3) Cり,) ×

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Q: Consider the points A(3, –3, 2), B(4,–5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: AB→ = i -2j-2kAC→ = -4i-j-2kAD→ = 3i+5j-5k Volume of parallelepiped with AB→, AC→ ,AD→ as adjacent…

Q: Consider the points A(3,-3, 3), B(4, –5, 1), C(-2,-4, 1), and D(6,3,-5). (a) Find the volume of the…

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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: Consider the points A(3, –3,5), B(5, –5, 2), C'(-1,–4, 2), and D(4, 1, –8). (a) Find the volume of…

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Q: The plane containing Q, S, A, U appears to be parallelto the plane containing which points?a. Q, E,…

A: The Parallel Plane: The Parallel planes are two planes that do not intersect. Since, this is cuboid.…

Q: A plane meets the coordinate axes in A, B, C. If the centroid of AABC is (a, b, c). Show that the…

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Q: Consider the points A(3, –1,3), B(4, –3,0), C(-2, –2, 0), and D(6,3, –5). (a) Find the volume of the…

A: given points A3,-1,3 , B4,-3,0 , C-2,-2,0 and D6,3,-5 (a) find the volume of parallelopiped that has…

Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of…

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, -4, 2), and D(4, 1, –8). (a) Find the volume of…

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Q: Consider the points A(2, –3, 3), B(3, -5, 0), C(-3, –-4,0), and D(3,3, -6). | (a) Find the volume of…

A: Note: According to our answering guidelines we have to answer only one question if multiple are…

Q: Consider the points A(3,-1, 3), B(4, -3,0), C(-2, -2,0), and D(6, 3,-5). (a) Find the volume of the…

A: Let's solve for volume and distance between point and plane.

Q: Consider the points A(2, –3, 3), B(3, –5,0), C(-3, –4,0), and D(3, 3, –6). (a) Find the volume of…

A: Given problem:-

Q: Consider the points A(3, -3, 2), B(6,-5,0), C(-1, -4,0), and D(6,3, –4). (a) Find the volume of the…

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Q: Consider the points A(1, -1, 2), B(2, –3,0), C(-1,-2,0), and D(2,1, –1). (a) Find the volume of the…

A: Here, the given vectors are: A(1,-1,2), B(2,-3,0), C(-1,-2,0) & D(2,1,-1) (a) Here,…

Q: Consider the points A(1, -1,4), B(2,-3, 2), C(-1, -2, 2), and D(4, 3, –6). (a) Find the volume of…

A: The answer is shown in step 2.

Q: Consider the points A(1, –1,4), B(2, –3, 2), C'(-1,–2,2), and D(4,3, -6). (a) Find the volume of the…

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Q: Given a triangle on the xy plane with the following coordinates for its vertices: A(2.5,1), B(1,3)…

A: Consider the given triangle with vertices A (2.5,1), B (1,3) and C (4,3) which is rotated on the xy…

Q: 3. Can a plane intersect two planes that are not parallel so that the inter- sections are parallel?…

A: To Explain: Whether it is possible or not that a plane intersects two planes that are not parallel…

Q: Consider the points A(3, –3, 3), B(4, –5, 1), C(-2, –4,1), and D(6,3, –5). (a) Find the volume of…

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Q: In a geometry class, students are asked to describe the dimensions of a plane based on the…

A: The statements given by students are Mark states that a plane has zero dimensions because it is made…

Q: Write a description of some model of Lobachevskian geometry. Specify the "plane surface" and what…

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