Find the volume of the parallelepiped with one vertex at (0, 0, 0) and adjacent vertices at (-3, 1, 4), (– 5, -5, 3), and (-5,0, 0).

Q: Find the coordinates of the centroid of the triangle with the given vertices. X(1, 4), Y(7, 2), Z(2,…

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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: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

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

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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: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: prove that the three planes 2x+y+z = 3 , x-y+2z = 4, x+z = 2 from a triangular prism and find the…

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: 2rydA, where D is the triangular region with vertices (0,0), (1, 2) and (0,3)

A: Dear Learner, We expert are following bartleby expert guidelines to answer the questions posted by…

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: This rectangular prism is intersected by a plane that contains point B,D,H, and F. What is the…

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Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

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

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

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Q: Find the distance between the point (5,-4, 1) and the plane containing the points (4, -2, 3), (-1,…

A: Here we have to find the distance between the point (5,-4,1) and the plane containing the points…

Q: 1. Find the area of the triangle in the R2 plane whose vertices are given by (0,0), (–1,4) and (7,…

A: 1. The Area of triangle with vertices (x1,y1),(x2,y2),(X3,y3) is given by formula : ∆…

Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

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Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

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: find the distance in space between the points (5,3,-2) and (0,0,1)

A: Use distance formula between two points

Q: Prove that the points 3,0),(4, 5),(-1, 4) and (-2,-1) taken in order, Lorm a rhombus, also find its…

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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: :) Find the area of the pentagon with vertices (0, 0), (4, 1), (1, 3), (0, 2), and (-1, 1).

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Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Use cross products to find the area of the triangle in the xy-planedefined by (1, 2), (3, 4), and…

A: Triangle T spanned by two non zero vectors u,v.  Then the area of the triangle is given     by :…

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 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: 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: A quadrilateral has the following vertices given:  P1 (1, 4), P2 (3, 4), P3 (3, 6), P4 (1, 6).  The…

A: Given points are :  P1(1,4) , P2(3,4) , P3(3,6) , P4(1,6). We will first plot those points in a…

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 centroid of the triangle if the vertices are  (0,0) , (4,0) and (0,6)

A: Given points are         0,0,4,0,&amp;0,6      And centriod G ?      centriod G= x1+x2+x33…

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: 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…

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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 area of the triangle with vertices (1,0,0), (0, 2,0), and (0,0, 1).

A: Area of triangle when three points are given is half the modulus of the cross product of the two…

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: 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: Consider the triangular region in the plane given by the triangle (1, 6), (6, -1), and (1, -4).…

A: See attached file for a step by step explanation.

Q: Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 2) and  (-1, 1)

A: Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 2) and  (-1, 1)

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…