Find the volume of the tetrahedron having the given vertices. (5, -5, 1), (3, -4, 4), (1, 1, 1), (0, 0, 1)

Q: Find the volume of the pyramid (tetrahedron) with vertices at the points: A(-3,2,1), B(12,-1,0),…

A: Given vertices of the tetrahedron: A-3,2,1, B12,-1,0, C3,1,0 and D1,1,5 a) The vertices can be…

Q: 5. How many rectangles would the net of a pentagonal pyramid have?

A: The net of a pentagonal pyramid consists of two pentagons and five rectangles .

Q: The base of a certain solid is the triangle with vertices at (-6, 3), (3, 3), and the origin.…

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Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

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Q: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 3,…

A: Consider the provided question, Let the vertices of the parallelepiped are A, B, C and D.

Q: A quadrilateral has vertices at (0,1,2), (3,0,1), (4,3,6), (2,3,2). Show that the volume of the…

A: A quadrilateral has vertices at (0,1,2), (3,0,1), (4,3,6), (2,3,2). Show that the volume of the…

Q: Find the volume of the tetrahedron having the given vertices. (4, -2, 1), (3, -1, 4), (1, 1, 1), (0,…

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Q: 24. Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,…

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Q: Find the volume of the tetrahedron with the given vertices. (1, 0, 0), (0, 2, 0), (0, 0, 1), (1, 2,…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the volume of the tetrahedron having the given vertices. (5, −5, 1), (3, −1, 4), (1, 1, 1),…

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Q: Find the volume of the tetrahedron having the given vertices (3, -3, 1), (3, -2, 4), (1, 1, 1), (0,…

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Q: Find the volume of the tetrahedron having the given vertices. (4, –4, 1), (4, –3, 4), (1, 1, 1), (0,…

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Q: Find the volume of the tetrahedron with the given vertices.(1, 1, 1), (0, 0, 0), (2, 1, −1), (−1, 1,…

A: The vertices of tetrahedron are A(1, 1, 1), O(0, 0, 0), B(2, 1, −1),C (−1, 1, 2) Then,

Q: Find the volume of tetrahedron given the following points (6, 7, 6), (8, 1, 9), (5, 7, 2), and (9,…

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Q: Find the volume of the parallelepiped defined by ?⃗= [1, 0, –4], ?⃗ = [8, –7, 9], and ?⃗ = [2, 3,…

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Q: Find the volume of the tetrahedron with the given vertices.(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1,…

A: We have given the vertices of tetrahedron; (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1) Since volume…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(5, 3, 5),…

A: Given three vectors, there is a product, called scalar triple product, that gives (the absolute…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS: P(-2,1,0), Q(2,3,2),…

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Q: the volume of tetrahedron having the vertices (3,-1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given vertices (3,-1,1), (4,-4,4), (1,1,1), (0,0,1) volume of tetrahedron is equal to 16 of the…

Q: Find the volume of the tetrahedron with the given vertices.(−3, −3, −3), (3, −1, −3), (−3, −1, −3),…

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Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0,…

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS…

Q: Find the volume of the tetrahedron with the given vertices. (4, 0, 0), (0, 4, 0), (0, 0, 4), (4, 4,…

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Q: Find the volume of a right triangular prism whose height is 4 and base is a right triangle with legs…

A: Find the area of base and then multiply the area with height.

Q: Find the volume of the parallelepiped with one vertex at (3, 2, 4), and adjacent vertices at (3, 6,…

A: Let, P=3,2,4, Q=3,6,5, R=-3,-1,-2, S=2,8,7 Now,…

Q: Find the volume of the tetrahedron having the given vertices. (4, -4, 1), (3, -5, 4), (2, 1, 1), (0,…

A: The given vertices are named as follows. P(4, -4, 1), Q(3, -5, 4), R(2, 1, 1) and S( 0, 0, 1).…

Q: Find the volume of the parallelepiped with one vertex at (4, 3, 1), and adjacent vertices at (6,…

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Q: Find the volume of the tetrahedron with the given vertices.(3, −1, 1), (4, −4, 4), (1, 1, 1), (0, 0,…

A: Find the vectors representing the edges of the tetrahedron.

Q: Find the volume of the tetrahedron with the given vertices.(0, 0, 0), (0, 2, 0), (3, 0, 0), (1, 1,…

A: The given vertices of a tetrahedron are (0,0,0), (0,2,0), (3,0,0) ,(1,1,4)

Q: Your job is to determine the coordinates of the remaining corners of the building; the side length…

A: given , Cube with A ,B ,C ,D are top vertex and A' ,B' , C' ,D' are the Down vertex that are touches…

Q: Find the area of the parallelogram with vertices (2,2), (4, 7), (5, 12), and (7, 17)

A: Given, The vertices of parallelogram (2,2), (4, 7), (5, 12), and (7, 17).  We have to find the area…

Q: Find the volume of the parallelepiped with the sides ü = (3,1,2), v =(4,5,1), w=(1,2,4). %|

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: Find the volume of a tetrahedron if the vertices are (1,1,1) , ( 5,-7,3) , (7,4,8) and (10,7,4)

A: Solution:- find position vector

Q: Find the volume of the parallelepiped with one vertex at (0, 0, 0) and adjacent vertices at (-3, 1,…

A: The vertices are given as , O=0,0,0 A=-3,1,4 B=-5,-5,-3C=-5,0,0  Find the volume of Parallelepiped.…

Q: Find the volume of the tetrahedron with the given vertices. (-3, –3, –3) (3, –1, –3), (-3, –1, –3),…

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Q: The volume of the parallelepiped whose adjacent edges are V = (2,3,4), ū = (1,2,–1) and w= (3,–1,2)…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(3, 4, 3),…

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Q: 2 Find the volume of the parallelepiped with sides u(1, -3, -1). v3(0. 4, -2). and न् 6. 3).

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Q: Find the volume of the tetrahedron with the given vertices.(5, 4, −3), (4, −6, −4), (−6, −6, −5),…

A: The vertices of the tetrahedron are: A(5, 4, −3), B(4, −6, −4), C(−6, −6, −5), D(0, 0, 10) We need…

Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given :  vertices of the tetrahedron are A(3, -1, 1), B(4, -4, 4), C(1,1,1) and D(0,0,1)   To find :…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(3, 0, 1), Q(2, 3,…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2,…

A: The given points P-2,-1,-3, Q0,2,0, R-3,-2,-4, S4,-3,-1

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: Find the volume of the tetrahedron with the given vertices. (4, 0, 0), (0, 2, 0), (0, 0, 1), (4, 2,…

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Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given vertices (3, −1, 1), (4, −4, 4), (1, 1, 1), (0, 0, 1)

Q: Find the volume of the tetrahedron having the given vertices. (4, -3, 1), (5, -4, 4), (2, 1, 1), (0,…

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Q: The vertices of a parallelepiped are, in no particular order, (4, –10, –21), (-11, –9, –17), (9,–3,…

A: Given a parallelepiped with its 8 vertices in no particular order. We need to find the volume of the…