The parallelogram (ABCD) has vertices at A(2,-1,4), B(1,0, –1), C(1, 2, 3), and D, then اخترأحد الخيارات 9. D = (1, –1, -4), projBÁ =(j + 2k) and area ABCD = 6 %3D D = (2, 1,8), projBÁ =(j+ 2k) and area of ABCD = 6/6 D = (1,-1,-4), projBÁ = 9(j - 3k) and area ABCD= V6 %3D D = (-2, 1, -8), projBÁ = 9(j – 3k) and area of ABCD= V6

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

A:

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: 5. Square JKLM with vertices J(-3, 5), K(0, 8). L(3, 5), and M(0, 2); 90° clockwise about P(-4, 0)…

A: If the point (-y,x) rotate 90 degrees clockwise about the point (a,b), then the coordinates of the…

Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

A:

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),…

A:

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: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

A:

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: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

A:

Q: Use v=&lt;3/5,4/5&gt;,w=&lt;-4/5, 3/5&gt;, to verify the Parallelogram Law

A: The given vectors are

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),…

A:

Q: Determine the coordinates for the intersection of the diagonals in RSTU with vertices at…

A:

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

A:

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

A:

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: Suppose that a box has its faces parallel to the coordinate planes and the points (4, 2,−2) and (−6,…

A:

Q: Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (7,6) ,…

A: Given:

Q: Find the areas of the parallelograms whose vertices are given in Exercises 35–40. 35. A(1, 0), B(0,…

A: Area of parallelogram ABCD is |AB x AD|

Q: Find the point R that breaks the directed segment PQ  in a ratio of 1:3, given point P(-4,5)  and…

A: Find the point R which breaks the segment PQ in the ratio 1:3 using section formula

Q: Find the coordinates of the point B that lies along the directed line segment from 3. A(-3,-2) to…

A: According to our company's guidelines, I can only answer first question since you asked multiple…

Q: A trapezoid is shown in the coordinate plane. 10 9- 8 7- 6- 5- 4 3- 2- -10 -9 -8 -7 -6 -5 -4 -3 -2…

A: Given is a trapezoid, when we divide it into 2 parts   equally, the left and right side will be…

Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

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

A:

Q: 4. 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:

Q: Verify that parallelogram ABCD with vertices A(-5, – 1), B(-9, 6), C(-1, 5), and D(3, – 2) is a…

A: We can verify this as below using the diagonals.

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

A:

Q: Find the area of the parallelogram with vertices P(2, 3, 3), Q(5, 5, 6), R(10, 9, 14), and S(7, 7,…

A:

Q: 2. Trapezoid QRST with vertices Q(3. 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

A:

Q: Verify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), B(—2, 3,…

A:

Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

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),…

A:

Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

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: Determine the coordinates for the intersection of the diagonals in RSTU with vertices at…

A:

Q: Find the point on the plane 2x + 2y + 5z = 2 that is closest to the point P(- 3, 5, – 5). (x, y, z)…

A:

Q: Find the distance between the planes 4x + 6y – 2z = 4 and –2x – 3y + z = -3.

A: We have to find out the distance between two planes

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

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,…

A:

Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

A:

Q: Find the angle between the planes (x+y+za1)and. (x-24+32-1). And find the Symmetricequations for the…

A:

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-6, -2,…

A:

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

A:

Q: I need help w/ following integration by pullback

A: Given that R be the parallelogram with the vertices at (1,0), (3,1), (4,4), (2,3). And…

Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

A:

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

A:

Q: A rectangle has a vertex at J(2, 2), H(4, −2), and G(−2, −5). What are the coordinates of the fourth…

A: You know that the diagonals of a rectangle bisect each other.