Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in length.

Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

A: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: Prove that llu - vll >=llull -llvll for all vectors u and v in Rn.

A: According to the given information, it is required to prove the inequality.

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

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Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

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Q: 1.Use vector methods to show that the diagonals of a parallelogram bisect each other. 2.Let…

A: We have to prove That Diagonals of a parallelogram bisect each other.

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: prove by vector method that diagonals of rectangle are equal in length and bisect each oth

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that ri+r2+r3 is equally…

A: given

Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: The cross product of two vectors in R yields a scalar. True False

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Q: The vectors u = and v= - are not parallel if and only if Select one: O True O False x = 18

A: I am attaching image so that you understand each and every step.

Q: Use the definition of the cross product to prove that the cross product of two parallel vectors is…

A: The cross product of two parallel vectors is zero. This can be proved by two definitions of cross…

Q: Find the area of the parallelogram whose diagonals are represented by the vectors a =(3,-3,1) and b…

A: See this solution in below

Q: Compute the distance between the vectors u = and v = 315

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

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: Let u and v be adjacent sides of a parallelogram. Use vectors to prove that the diagonals of the…

A: Vectors are quantities that have both magnitude and direction. We can add two vectors, and to the…

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

A: Let the arbitrary triangle has vertices A, B and C has three vectors AB, →AC →  and  BC → . Let M…

Q: If the vectors a and b are such that a = kb where k is a positive scalar, then the vectors a and b…

A: Given statement: If the vectors a and b are such that a=kb where k is apositive scalar, then the…

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

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Q: Use a directed line segment to represent the vector.v = (−2, −5)

A: Let the given vector : Here, -2 represents x-cordinate and -5 represents y-cordinate.

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Two nonzero vectors are perpendicular if and only if their _____ _______ is equal to______.

A: Given:Two nonzero vectors are perpendicular if and only if their ______is equal to ______

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

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Q: Find the volume of the parallelepiped defined by the vectors: a= (3, -1, 1), b= (4,0,2) and c=…

A: Given are the vectors  a= (3, -1, 1), b= (4,0,2) and c= (-1,-2,-3) The objective is to find the…

Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: Use a directed line segment to represent the vector.u = (2, −4)

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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 whose diagonals are represented by the vectors a = (3,-3,1) and b…

A: As we know that; The expression for the area of the parallelogram with the diagonals a→ and b→.…

Q: Find the area of the parallelogram spanned by the following vectors. u = [4, –6, 5] v = [0, 6, 8]…

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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Find the area of the parallelogram defined by the vectors (9,1) , (-5,5)

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero