Find a vector å with representation given by the directed line segment AB, for A(-1, 1) and B(3, 2). Draw AB and the equivalent representation starting at the origin.

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

Q: Find a vector a with representation given by the directed line segment AB, where A(-2, -2) and B(4,…

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Find a vector a with representation given by the directed line segment AB. A(0, 4, 2), B(4, 4, –1)…

A: Given vectors

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find a vector a with representation given by the directed line segment AB. A(3, 0, -4), B(3, 4, 4)…

A: The given points are: A3, 0, -4, B3, 4, 4 Vector AB can be represented as vector is AB so the tail…

Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: Verify the orthogonality p

A: answer is in next step

Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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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: Find a vector a with representation given by the directed line segment AB. A(-1, 5), B(2, 4) Draw AB…

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Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: Find a vector a with representation given by the directed → line segment AB, where A(−5, 0, 1) and…

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Q: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

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Q: Find a vector a with representation given by the directed line segment AB, where A(-4, 0, 1) and…

A: A=-401,  B=18-1 the vector a is given by  a=B-A

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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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: The parallelogram shown here has vertices at A(2, -1, 4),B(1, 0, -1), C(1, 2, 3), and D. Find the…

A: given: a figure showing parallelogram having the vertices A(2,-1,4), B(1,0,-1), C(1,2,3) and D. we…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: Find a vector a with representation given by the directed line segment AB. A(-4, -2), В(2, 5) Draw…

A: A vector from point A (x1,y1), to point B (x2,y2) is given by AB =(x2-x1)I +(y2-y1)j

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Find a vector a with representation given by the directed line segment AB. A(5, 4), B(0, 8)

A: We have to find a vector a with representation given by the directed line segment AB.

Q: Find a vector a with representation given by the directed line segment AB, where A(−5, 0, 1) and…

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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: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given that L is a line in 2-space or 3-space that passes through the points A and B then the…

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Find a vector a with representation given by the directed 个 line segment AB, where A(–6, −6) and…

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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 vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

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

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Q: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

Q: Find a vector a with representation given by the directed line segment AB. A(-1, 4), B(1, 5) Draw AB…

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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

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

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Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: Let P be the plane through (1, 2, 3), (4, 3, 3), and (4, 4, 1). Find the vector of length 2 that is…

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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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: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: Find a vector a with representation given by the directed line segment AB. А(О, 3, 2), в(1, з, -5)…

A: Consider the given line segment AB→. A(0,3,2) and B(1,3,-5). Let AB→ be  a vector from A to B and…

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

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: Find a vector a with representation given by the directed line segmer (-6,0, 3) and B(1,8, –1).

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Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned the…

A: Observe that the parallelogram is spanned by the vectors. &lt;-8,9&gt; and &lt;7,2&gt;

Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step