Suppose that a parallelogram is bounded at one vertex by the vectors i = |,3 = ,: Find the area of the parallelogram. Draw the graph below.

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

A: Now

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: Consider the parallelogram given by vectors [12, 5], and [18, 0]. Give the lengths of the altitudes…

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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: For the three vectors a, band, it is found that ax statement below is true?

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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: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v, and w…

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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: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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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: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

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: 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: What is the area of the parallelogram determined by the vectors v = (1, 3, 6) and w = (-1,0, 3)?

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Q: If vector v is represented by an arrow, how is -3v represented?

A: Given: If vector v is represented by an arrow. To find: How is -3v represented?

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: 5. N(2,-2), P(1,-4). Q(7,-4), R(6,-2) along (4, 5

A: Vertices of image are - N(2,-2); P(1,-4); Q(7,-4); R(6,-2) Vector - (4,5)

Q: If two planes are not parallel then the in a

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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 area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

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: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

A:

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

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: By vector methods, show that the line segment joining the midpoints of two sides of a triangle is…

A: To prove :- The line segment joining the midpoints of two sides of a triangle is parallel to the…

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

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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: 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: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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

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

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

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Q: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

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 a vector that is oppositely directed to v = with a length of V3

A: We have to find the vector by given data

Q: Show that direction vectors of the lines L: and are arthogonal.

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

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