a) Find the vector component of L =<-1,2,5 > along A =< 1,–1,2 > and orthogonal to L. b) Find the area of the triangle with verticesA(5,0, 3), B(-2, 10, 4) andC(1,–2,–1). c) Determine whether the vectors lie in the same plane p=< -1,2,0 >,q =< 1,0, –9 >,r =< 0, –8, 10 >.

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

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Q: sider the following coordinates and vectors, A(-2, 1, 0), B(2, -2,0), u = 3i + 2k, v = 4i + 7j+5k,…

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Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

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Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: Consider the parallelepiped determined by the vectors A = (3, 1, 0), B = (1, 3, 0) and C= (1, 1, 1).…

A: Consider the parallelepiped determined by the vectors   a=⟨3,1,0⟩, b=⟨1,3,0⟩ and c=⟨1,1,1⟩ The…

Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: Given two vectors P=a,-a, Q-2а, -а, ta, R=2a,+3a,+a, Determine: (a). (P+Q)x(P-Q) (b). Q.RxP (c)…

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Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Suppose that v₁ = (4, 4, 0, 7), v₂ = (2, -5, 5, 4) and v3 = (-7, 0, 5, 2). Is the following vector…

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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 the area of the parallelogram defined by the vectors Area = 1 -2 2

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.