Prove that the diagonals on the parallelogram in the figure intersect at their midpoints. (b, c) (a+b, c) (0, 0) (a, 0)

Q: Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7)…

A: NOTE: Refresh your page if you can't see any equations. . given vertices are

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Determine if the planes 3x + 2y- z 7; x-9y+ 2z 0 are parallel, orthogonal, or neither. If they are…

A: We will one by one check whether the planes are parallel, orthogonal. And then we I'll find the…

Q: Find an equation of the plane determined by the points P(1,2,3), Q(2,0, 1), and R(0, –-1,1).

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Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Verify that the two planes are parallel.

A: -x+6y+3z = 6-13x +2y+z = 7∵-1-13=62=31=3then the planes are parallel

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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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: 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: Use vectors to show that the points form the vertices of a parallelogram. (2, 9, 1), (3, 11, 4), (0,…

A: Given: A=(2,9,1) ,B=(3,11,4),C=(0,10,2),(1,12,5) To Show: Given points form the vertices of a…

Q: Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in…

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Q: Find the distance from the point A(2,4,3) to the plane determined by the three points B(1,4,2),…

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: Verify that the two planes −3x + 6y + 7z = 1 , 6x − 12y − 14z = 25 are parallel and find the…

A: Given equations of two planes are: -3x+6y+7z=1 and, 6x-12y-14z=25 Thus we can define the normal…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (2, 5, 3), Q = (– 3, –…

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Q: Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the…

A: Let us consider an incomplete regular polygon of n sides and the same polygon after rotation. We…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Determine whether the planes are parallel, perpendicular or neither. 5x + 2y+ 3z = 2 y= 2x + 3z

A: Given 5x+2y+3z=2y=2x+3z

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: Which of the points A(-4, 0, -1). B(3, 1, -1), and C(2, 4, 6) is closest to the yz-plane? Which…

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Q: Use the cross product to find an equation for the plane that passes thru the points (1, 2, 3), (4,…

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Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

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Q: Write the characterisation of two parallel planes (given in general forms) in terms of the cross…

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Q: Show that the planes given by 2x − 4y − 3z = 5 and −4x + 8y + 6z = 1 are parallel, and find the…

A: Solution:Given2x − 4y − 3z = 5 −4x + 8y + 6z = 1To prove :The planes are parellel and to find the…

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ‹6, 2, -1›,     b…

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Q: Find the distance between u and v and determine whether u and v are orthogonal, parallel, or neither…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A: The objective of the question verify the parallel of given plane and find distance between them .

Q: Suppose that a parallelogram is bounded at one vertex by the vectors i = |,3 = ,: Find the area of…

A: Area of parallelogram =|u×v| ,where u and v are the vectors which represent the side of…

Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: -6x - Find dA, where Ris the parallelogram enclosed by the lines -3x+y R – 6x – y = 0, – 6x – y = 2,…

A: I have used jacobian to solve the area of above double integral.thanks

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Use vectors to show that the triangle with vertices (-2, 2), (4, 10), and (20, –2) is a right…

A: vector method to find right angle triangle.

Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 7y + 7z = 1, 7x – 7y + 7z…

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Q: (2, 1) is the midpoint of AB, in which A has coordinates (8, 10). Find the coordinates of B.

A: given: (2,1) is the mid point of AB. the coordinates of A are (8,10) we have to find the coordinates…

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A: Using distance formula between parallel planes

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

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Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…