Calculate the volume of a parallelepiped if four of its eight vertices a A (1, 2, 4), B (2, 0, 5), C (7, 1, -2) and D (4, 3, 1).

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: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-7, 5,…

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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: Determine the volume of the parallelepiped whose sides are represented by the following vectors: Á =…

A: We need to find the volume of the parallelepiped . The formula for the volume of a  parallelepiped…

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

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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: Hi, any help with this calc 3 problem would be great, thank you!

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Q: Find the area of the parallelogram with vertices  K(2, 1, 1), L(2, 2, 4), M(4, 6, 4), and N(4, 5,…

A: To Determine  The area of the parallelogram with vertices  K(2, 1, 1), L(2, 2, 4), M(4, 6, 4), and…

Q: Find the area of the parallelogram with vertices (1, 1, 1), (–6, 4, 1), (5, 3, 4), and (–2, 6, 4).

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Q: Find the areas of the parallelograms whose vertices are given A(0, 0, 0), B(3, 2, 4), C(5, 1, 4),…

A: Given: The vertices of parallelogram are A(0,0,0) , B(3,2,4) , C(5,1,4) and D(2,-1,0) To find: Area…

Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

A: We know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the area of the parallelogram whose vertices are listed. (-1,0), (3,7), (7, –2), (11,5)

A: Consider the vertices of the parallelogram ABCD is A=-1,0,B=3,7,C=7,-2,D=11,5

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 with vertices K(3, 2, 1), L(3, 5, 3), M(5, 10, 3), and N(5, 7,…

A: To find the area of the given parallelogram, use the vector method which is described as.We know…

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

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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 area of the parallelogram with vertices K(1, 2, 1), L(1, 5, 2), M(6, 10, 2), and N(6, 7,…

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

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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: 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: Find the area of the parallelogram with the vertices A(2, 2), B(1, 4), С(3, 5).

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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: Calculate the volume of a parallelepiped if four of its eight vertices are А (-1, 2, 4), В (1, 4,…

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Q: If the interval [1, 9] is partitioned into 4 subintervals of equal length, what is ∆x? List the grid…

A: Since n = 4 on the interval 1, 9 then                                               ∆t=b-an=2 where…

Q: Determine the area of the quadrilateral having (8, -2), (5, 6). (4, 1), and (-7, 4) as consccutive…

A: The Area of the quadrilateral whose coordinates of vertices are of the form x1,y1, x2,y2,…

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 parallelepiped defined by the vectors: a= (3, -1, 1), b= (4,0,2) and c=…

A: Given are the vectors a=3,-1,1, b=4,0,2 and c=-1,-2,-3 The objective is to find the volume of the…

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 area of the parallelogram with vertices P(1, 3, 2), Q(2, 6, 4), R(4, 12, 12), and S(3, 9,…

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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 area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: Chapter 11, Section 11.4, Question 033 Use the fact that the volume of a tetrahedron with adjacent…

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Q: Find the area of the quadrangle with vertices (6, 1), (-5, 5), (–3, –5), and (5, –4). Area = 1,0 -7…

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Q: Find the area of the parallelogram with the points A(2, 5, 6), B(4, 8, 10), C(11, 7, 9) and D(9, 4,…

A: Formula: The area of parallelogram = Length of cross product of adjacent sides. Given: Vertices of…

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

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Q: Show that the quadrilateral having vertices at (1, −2, 3), (4, 3, −1), (2, 2, 1) and (5, 7, −3) is a…

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Q: Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1),…

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Q: Find the area of a parallelogram with corner points at (2,4), (5,9), (9,9), and (6,4) Area

A: Area of a parallelogram of base b units and height h units is given by the equation; Area (A)=a·h

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: A parallelogram has 2 vertices (1,1) and (0,7) and their diagonals intersect at the point (4,3).…

A: Given:

Q: Find the area of a parallelogram whose vertices are (- 2, – 3, 2), (2, – 4, 2), (2, 2, 0), and (6,…

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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: A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral…

A: slope of the line joining (x1,y1),(x2,y2)  is y2-y1x2-x1

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…