Calculate the volume of a parallelepiped if four of its eight vertices are А (-1, 2, 4), В (1, 4, -5), С (3, 1, -2) and D (-4, 5, 1).

Q: find the area of the parallelogram whose vertices are listed. (0,0), (-2, 4), (4, -5), (2, -1)

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

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: Find the volume of the parallelepiped determined by the vectors a = (5, 2, – 1), b = (0, 4, 1), č =…

A: We will find the volume of the parallelepiped by using the given vectors.

Q: 2. Find the volume of the parallelepiped having a = (1,4,–7), b = (2,–1,4) and c = (0,-9,18) as…

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Q: Find a plane through the points (3,2,3), (4,-3,-3), (4,4,1)

A: The given points are: (3, 2, 3),  (4, -3, -3),  (4, 4, 1)

Q: Find the volume of the parallelepiped with corresponding vectors 〈2,1,0〉,〈-1,2,2〉and〈0,-2,1〉

A: Let's find.

Q: | The vertices of a parallelepiped are, in no particular order, (4, –10, –21), (-4, –16, –14),…

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Q: Find the volume of the parallelepiped determined by the vectors u = (1,2,-3), v = (2,4,-1), and w=…

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Q: Compute the volume of the parallelepiped dened by the vectors v1 = (1, 3, 1), v2 = (2, 1, -1) and…

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Q: |Find the coordinates of the intersection of the diagonals of paralle with vertices P(2,5), R(3,3),…

A: Follow the procedure given below.

Q: Find the volume of the parallelepiped determined by the vectors = (1, 2, 3), b = (3, 0, 6) and c =…

A: This question is related to vectors, we will solve it by using the formula of volume of…

Q: Calculate the area of the parallelogram with the given vertices: (-1,-2), (2,7), (7,2), (10,11).

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Q: Find a plane containing the point (– 3, – 3, 7(t) = (– 2, – 3, – 5) + t(3, 4) and the line 6, 7).

A: we have to find the equation of plane that contains the point (-3,-3,-4)  and the line…

Q: Find the area of parallelogram whose vertices are listed. (0,0), (5,2), (6,4), (11,6).

A: area of parallelogram = 2*area of triangle area of triangle = (1/2)[ 5 2 1]…

Q: Find the volume of the parallelepiped determined by the vertices A(1,1,1), B(4,7,2), C(3,2,1) and…

A: Let the vertex A(1,1,1) be taken as the point from which all measurements are taken. Calculate AB→,…

Q: find the area of the parallelogram whose vertices are listed. (0, -2), (5, -2), (-3, 1), (2, 1)

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), В(-4, -5,…

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Q: Find the area of the parallelogram with vertices (2, 3),(5, 3), (4, 5), (7, 5).

A: Given: Vertices of parallelogram is: 2, 3, 5, 3, 4, 5, 7, 5

Q: Calculate the volume of a parallelepiped if four of its eight vertices a A (1, 2, 4), B (2, 0, 5), C…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will simply use…

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: Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum…

A: Let the sides of the parallelogram be 'l' with longest and 'b' with shortest parallel lines and…

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 parallelepiped with the given vertices . (0, 0, 0), (0, 4, 0), (-3, о, 0),…

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Q: Find a homogeneous system whose solution space is spanned by the following sets of three vectors:…

A: This question is related to linear algebra.

Q: Calculate the volume of a parallelepiped if four of its eight vertices are A (-5, 3, 1), В (1,-2,…

A: We have to find the volume of a parallelepiped when it's four vertices are given .

Q: Prove analytically that if the diagonals of a parallelogram rectangle. are equal, then the…

A: Given:-  Diagonals of parallelogram are equal.To proof  Parallelogram is a Rectangle.

Q: Determine the volume of the parallelepiped formed by the vectors P = (2,4,3), Q = (1,3,2) and R=…

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Q: Find the volume of the parallelepiped defined by the vectors 5 5 5 ne =

A: To find: The volume of parallelepiped defined by three vectors 0-15, 55-3 and 5-4-2. Concept used:…

Q: Find the volume of the parallelepiped with the given vertices . (0, 0, 0), (0, 4, 0), (-3, 0, 0),…

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Q: |The vertices of a parallelepiped are, in no particular order, (4, – 10, –21), (-4, –16, –14), (2,4,…

A: We have to find the volume of the parallelepiped with vertices 1.…

Q: Find the volume of the parallelepiped divined by the vectors  [5]   [0]  [4] [3],  [4], [-1] [-1]…

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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: The vertices of a parallelepiped are, in no particular order, (4, –10, –21), (-4,–16, –14), (-11,…

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Q: Calculate the volume of a parallelepiped if four of its eight vertices are A (1, 2, 4) , B (2, 0,…

A: Given that: A(1,2,4), B(2,0,5), C(7,1,-2) and (4,3,1)

Q: Find the volume of the parallelepiped determined by the vectors (0, 4, 5), (2, 0, 5), and (-1, 3,…

A: Volume of parallepiped is (a X b).c

Q: Find the volume of the parallelepiped defined by the vectors 2 4 -4 -2 4 3.

A: We have to find volume

Q: Find the volume of the parallelepiped determined by the vectors a= (3, 2, - 1), b = (0, 4, 3), č =…

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Q: Prove that cyclic parallelogram is a rectangle.

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Q: Find the area of the quadrangle with vertices (4, 1), (-5, 4), (-3, –6), and (3, –3). 1,0 Area =

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Q: The vertices of a parallelepiped are, in no particular order, (4, –10, –21), (-4,–16,–14), (2, 4, –…

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Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1) and M(-1, 2) is a square. 10 4…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the volume of the parallelepiped with the given vertices . (0, 0, 0), (0, 4, 0), (-3, 0, 0),…

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Q: Show that the quadrilateral having vertices at (1, 1,3), (-2,1,-1), (-5,4, 0), and (-8, 4,-4) is a…

A: This is a problem related to area of the parallelogram by cross products. Based on the general…

Q: What is the area of a parallelogram if the coordinates of its vertices are (2, 1), (8, 1), (11, 5),…

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Find the area of the parallelogram defined by the vectors (9,1) , (-5,5)

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Q: Find the area of the parallelogram with vertices (9, –3, –1), (6, –8, –1), (13, –1,4), and (10, –6,…

A: Use distance formula and multiply.

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…

Q: Find the area of the parallelogram with vertices at (1, -1), (13, −11), (−4, −1), and (8,–11). Area…

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