Points A(2,0,0), B(2,2,0), C(0,2,0), D(0,2,2), E(0,0,2), and F(2,0,2) are the six corners of a cube and points P, Q, and R are the midpoints of AB, CD, and EF, respectively. Using cross product, find the area of the triangle formed by the points P, Q, and R.

Q: 3) In the coordinate plane, quadrilateral ABCD has vertices A(-2, 3), B(4, 5), C(10, -1), and D(8,…

A: We can state the defining property of a parallelogram as follows:" If a quadrilateral is a…

Q: Use drawings as needed to answer the given question

A: (a) In Euclidean geometry, if two or more than two points lie on a line close to or far from each…

Q: Find a such that the points A(1, 5), B(4, 7), and C(a, a) are collinear. a =

A: Solved below

Q: Parallelogram ABCD has diagonals AC and BD that intersect at point E as shown. Which of the…

A: Given that:

Q: Given the coordinate of one endpoint of AB and its midpoint M, find the coordinates of the other…

A: If co-ordinates of A is (x1,y1)and co-ordinate of B is (x2,y2)then midpoint of AB isx1+x22,y1+y22

Q: Find a such that the points A(1, 3), B(4, 5), and C(a, a) are collinear.

A: Explanation: Given that,  Three points  A(1,3)B(4,5)C(a,a) We know that,  If three points are…

Q: Interpreting as area, Sº3 V9 – a² dæpresents A. Area of a quadrant of the circle with center at the…

A:

Q: Points A(2,0,0), B(2,2,0), C(0,2,0), D(0,2,2), E(0,0,2), and F (2,0,2) are the six corners of a cube…

A: We know that midpoint of line segment joining x1,y1,z1 and x2,y2,z2 is x1+x22,y1+y22,z1+z22 Now, P…

Q: Quadrilateral EFGH has the vertices E(0, 0), F(a, 0), G(a + b, c), and H(2b, 2c). Verify that EFGH…

A: Given, EFGH is a quadrilateral which has vertices E(0,0), F(a,0), G(a+b,c) and H(2b,2c)

Q: using green's theorem calculatefx'd +(4x + y ky ,where c is the vertex of the triangle (0,0),(1,2)…

A:

Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Parallelogram JKLM has vertices J (0,0), K(2,2), L(x,y), and M (5,0). Find (x,y).

A: Given vertices of parallelogram are J(0,0),K(2,2),L(x,y),M(5,,0)

Q: Use dot product to find the interior angles at A, B, and C of the triangle defined by the three…

A:

Q: Prove that the figure with the coordinates given is a rectangle. A(– 7,2),B(2,8), C(6,2),D(– 3, –

A: on solving this we get the

Q: Triangle ABC is shown in the following xy-plane with A(2,3) ,B(20,11), and C(16,3) What is the area,…

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Q: Sections ABCD is a quadrilateral having the given coordinates A(2, 3), B(8, 9), C(11, 3), and D(11,…

A:

Q: In this exercise we find the area of a plane figure. Draw the parallelogram with vertices  A(1, 5),…

A: According to question given that vertices of the parallelogramA(1,5), B(5,5), C(3,7), D(7,7)

Q: Find the area of the triangle with the given vertices. Hint: -||u x v|| is the area of the triangle…

A: In this question we have to find the area of the triangle.

Q: Use dot product to find the interior angles at A, B, and C of the triangle defined by the three…

A: HINT:  To calculate the angle we need the following thing: cos(α) = A.BAB We need to calculate AB…

Q: Find the area of the triangle P QR with vertices P (1, 1, 0), Q(7, 1, 0) and R(9, 4, 2). (Your work…

A:

Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: 3) FIND THE COORDINATES OF THE MIDPOINT OF AB WITH ENDPOINTS A(-8,2) AND B C0,4).

A:

Q: The table below shows the coordinates of triangle RST and the coordinates of R' in triangle R'ST.…

A:

Q: In triangleRST, the medians are RM, SN, and TP. If RM = 9, SN = 12, and TP = 16, find the distance…

A: median of the triangle

Q: The corners of a quadrilateral are (4, 0), (12, 4), (10, 8), and (4, 4). How far is its centroid…

A: Given data is: The corner points of a quadrilateral are 4,0, 12,4, 10,8, and 4,4 To find how far is…

Q: find the distance d between the points P1 and P2, P1 = (a, a); P2 = (0, 0)

A: Since, we know that the distance between two points A and B havingcoordinates (x1,y1) and (x2,y2) is…

Q: Find the cross product a × b. a = i + et j + e−t k,      b = 7i + et j − e−t k

A: Ans:  We have to find the cross product a→×b→         a→=i+etj+e-tk; b→=7i+etj-e-tk

Q: Ex: Find the area of the triangle with vertices P(1,-1,0), Q(2,1,-1) and R(-1,1,2). Area of the…

A: The vector A=a1i⇀+a2j⇀+a3k⇀ and B=b1i⇀+b2j⇀+b3k⇀ then the vector AB⇀ is given by…

Q: The area of the triangle with vertices at P = (1, 0, -2), Q = (2, 3, 1) and R = (2,1,0) is O a) V14…

A:

Q: Line segment AB is drawn on the grid with endpoints at A (0,8) and B (6,0). Using a straightedge and…

A:

Q: The parallelogram ABCD has vertices A (3, 2, 0), B (7, –1,–1), C (10, –3, 0) and D (6, 0, 1).…

A: We have AB⇀=(7,-1,-1)-(3,0,2)=(4,-1,-3)AD⇀=(6,0,1)-(3,0,2)=(3,0,-1) So we get AB⇀ ×…

Q: Find the area of a triangle formed by the lines 2x + 3y = 24, I- 2y = -9 and the y-axis. O 21/2 sq.…

A:

Q: Show that the lines 2x+3y-2=0, 3x-2y+23=0 and x-5y+12=0 are the sides of an isosceles triangle. Find…

A: Plot the given 3 st. lines and mark the intersection points forming the triangle.

Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are twice as far from the…

A: a) Suppose the distance between two points  A(x, y, z)  and the origin   Plug into the distance…

Q: Find the distance between u and v.

A: To find the distance between vectors u and v. We know that the distance between two vectors A=x1y1…

Q: Ex.: Find the area of the triangle whose vertices are A(1,-1,0), B(2,1,-1) and C(-1, 1,2).

A:

Q: Segment IJ I(-6,-12) J(-18, 22)

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Q: J is the midpoint of IK andG is the midpoint of HK. If HI = z- 61 and GJ =Z- 63, what is GJ? I K GJ…

A:

Q: Find the area of the parallelogram with adjacent sides u = -7i + 7j + 7k and v = 9i – 6j + 8kļ. Area…

A:

Q: Find the coordinates of the midpoint of AB. 3. A(0, 0), B(8, 2) 4. A(4, 7), B(2, 13) 5. A(-3, -6).…

A: We have to find the coordinates of the midpoint of AB¯ where coordinates of points A and B are given…

Q: The distance between the points (3, 8) and (x, 8x + 3) i

A: Solve for the distance between two points

Q: (a) With usual notations, show that the circumcenter G of a triangle AABC is given in barycentric…

A: Condider the figure: The circuncenter G. If R is the circumradius, the coordinates of G…

Q: A={d,e,f}, B={3,4}. Find the Cartesian product dXe and eXd

A: Given that: A=d,e,fB=3,4 To find the cartesian product

Q: The plane can perpendicular to the a) x-axis at (3, 0, 0) b) z-axis at (0, 0, -2) c) y-axis at (0,…

A:

Q: AABC is dilated from center A by a factor not equal to 1 to form AAK L. Which of the statements must…

A:

Q: Quadrilateral WXYZ with vertices W(-3, 8), X(2, 5), Y(-1, 2), and Z(-6, 0); translated ald the rule…

A: Given: The quadrilateral WXYZ with vertices W(-3, 8), X(2, 5), Y(-1, 2), Z(-6, 0). The translation…

Q: Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular…

A: Given:point A(-5,3),B(9,-9)         arbitrary point p(x,y) is on perpendicular bisector 'l'we know…

Q: Find the cross product a x b. a - (t, t?, ), b- (1, 30, 722) b = (1, 3t, 72)

A: Given that the vectors are  a = t, t2, t3   and    b = 1, 3t, 7t2 We need to find cross product a x…

Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: Use the Distance Formula to determine the type of triangle that has these vertices: a) A(0, 0), B(4,…

A: Note: Since you have asked multiple questions. We will solve the first question for you. If you want…