Using vectors, prove that the diagonals of a rhombus are perpendicular

Q: Find the dot product of the vectors. v = i + 5j; w = -i + j %3D V. W = Submit Answer

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Q: Determine whether the statement is true or false. The vector (3, -2, 4) is parallel to the plane 6x…

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Q: ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC.

A: Given: ABCD is a quadrilateral where AB=DC and AB parallel to DC. Prove: AD=BC and AD parallel to…

Q: Prove the stated property of distance between vectors. d(u, v) = d(v, u) for all vectors u and v

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Q: Using vectorsProve that the diagonals of a parallelogram bisect each other

A: Using vectors we need to prove that the diagonals of a parallelogram bisect each other.

Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i+j and i – 2j as…

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Q: Find the measures of the angles of the triangle where vertices are A = (-1,0), B = (2,1), C =…

A: Given: The vertices of the triangle are: A=-1, 0B=2, 1C=1, -20

Q: Let triangle ABC: |AB| = b,|AC| = č. Express the vector h, directed along the height of AH, using of…

A: Given triangle is ABC. Here, AB=b and AC=c Also, diagram is given as, The objective is to express…

Q: Find the vectors u + v, u-v, and 5u | u = i + j, v = -j – 2k %3D u + v = u - v = 5u

A: The given vectors are

Q: . Proof Use vectors to prove that the diagonals of arhombus are perpendicular.

A: For any rhombus, We can take the vertices to be the origin, and the points a, b, and a + b in r2.…

Q: nts A, B, C, D are positioned such that the line AB is perpendicular to CD, and BC is perpendicular…

A: In the following question, the concept of the dot product is applied. Dot Product The product of the…

Q: The three vertices of a triangle are located at A(6,-1,2), B(-2,3,-4), area of the triangle; (c) a…

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Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The area of the parallelogram determined by the vectors u and v is A=u×v. Given u = i + j and v = j.…

Q: Investigate the dot products a. (a x b) and b. (a x b) for any two vectors a and b in three-space.…

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Q: Find the measures of the angles of the triangle where vertices are A =(-1,0), (2,1), C = (1,-20).…

A: The given triangle will be

Q: Using vectors, prove that if the diagonals of a rectangle are perpendicular, then the rectangle is a…

A: To Prove- Using vectors, prove that if the diagonals of a rectangle are perpendicular, then the…

Q: Determine whether the given vectors are perpendicular. = (0, –7), 3 (8, 0) y = O Yes O No

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Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? EN B 3 4 nob C…

A: Given:

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

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Q: The vectors į+j and i-į are perpendicular. True False

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Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The vectors u, v, and w. u=i+j-k,v=2i+j+k,w=-i-2j+3k.

Q: Determine whether the given vectors are perpendicular. u = 2i, v = -i + 8j %3D %3D Yes No

A: The given vectors are u=2i and v=-i+8j

Q: Use cross products to determine whether the points A, B, and C are collinear. A(- 6, - 5,1),…

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Q: In parallelogram ABCD, E is the midpoint of the diagonals. Тext Let AD = ū and AB = v. A D Express…

A: AD⇀=BC⇀=u⇀ AB⇀=DC⇀=v⇀

Q: True or false?(a) The vectors v and −2v are parallel.(b) The vectors v and −2v point in the same…

A: The vectors v and −2v are parallel. Since the corresponding components of the vectors v and −2v are…

Q: Let a,b be scalars. Find a vector perpendicular u=

A: Given u = <a,b>                   a,b are scalarlet v be the vector perpendicular to uv =…

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: The directed line segment from the point A to the point B in the Cartesian plane is the vector 1/2

A: We have to check given statement is true or false.

Q: Owing vectors is perpendicular to the line L: 2x +3y- 6 = 0 2i + 3j O 2i - 3j (후 +1를 이 rious

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Q: pute u + v and u - 2v. 目 …日 olay the following vectors using arrows --2v, u + v, u- v, and u- 2v.…

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Q: 1 Let vi 6 and v3 7 V2 -1 4 3

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Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: The vertices of a triangle in space are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Explain how to…

A: Given:

Q: Prove the stated property of distance between vectors.d(u, w) < d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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Q: Consider some perpendicular unit vectors vi, v2, .. , Vm in R". Show that these vectors are…

A: We have to prove that given perpendicular unit vectors are linearly independent.

Q: The area of the parallelogram with vectors R(1,2,-1), P2(4,2,-3), P3(6,-5,2).P4(9,-5,0) is a) 998 b)…

A: Consider the given vectors P11,2,-1,P24,2,-3,P36,-5,2, and P49,-5,0. Use the given vectors and draw…

Q: answer above is NOT correct. d three vectors v1, v2, V3 such that (1) any two span a ne, and (2)…

A: Plane and spanning vectors

Q: Find the real part of the length of the vector v° = (5 + i, –3 – i)

A: Use the given vector.

Q: B 2 and i = 6 Let y = Write j as the sum of a vetor in Span {ū} and a vector orrhogonal to ủ.

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Q: Using vector, prove that the base angles of an isosceles triangle are equal.

A: Given  Triangle given is isosceles. Prove Base angles are equal.