Let u = (1, -3, 2), v = (3, -3, 5) and w = (2, 5, -4) be vectors in R. a) Determine whether the angle between v and w is right, acute or obtuse. b) Compute the vector of length 15 that is pointing in the same direction of z. c) Compute the volume of parallelepiped formed by vectors u, v and w.

Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

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Q: 5) Let A = (4, 1,2) and B= (1,2,-1). Find: a) ProjAB ProjBA b) all nonzero vectors X in R³…

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Q: ● Let u = 2-25 - 2k + ● and = 2î - 2Ĵ+k. Find a vector w such that the parallelepiped spanned by u,…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: A parallelipiped is constructed using vectors (8.1,2.3,0), (9.5,2.0,0) and (7.3,-2.1,7.7), what is…

A: To find the volume of parallelepiped.

Q: Find the volume of the parallelepiped that the vectors u, v, and w generate.

A: We recall formula and then solve this problem.

Q: Prove that the angle between two unit vectors u1, and u2, in R" is arccos(u1 * - u2,).

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Q: Find the angle between the given vectors:  a) u=(3,4), v=(5,-12); = x1y1 +x2y2 b) u(1,1,1),…

A: Sol:- a) u=(3,4), v=(5,-12); <u,v> = x1y1 +x2y2 i.e a)  u=(3,4,0), v=(5,-12,0); <u,v> =…

Q: 4.) Here are three vectors in R": (1,2,0,3), (2,1,3,2), (0,0,1,2) Find the three dimensional volume…

A: The given vectors in ℝ4 are 1, 2, 0, 3T, 2, 1, -3, 2T, 0, 0, 1, 2T. We have to find the volume of…

Q: Let u = i +2j-5k, v = 10k - 2i - 4j and w=-i-2j+ak, with & E R. a) Without calculation, state with…

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Q: a) Find the area of the triangle with vertices A(-2,5,1), B(3,-5,-2) and C(3,2,-4) using vector…

A: see below the answer and calculation

Q: 10. Given à = (3,-1,5) and b = (2,1,-8), find: a) 3ā + 25 Ans: b) āxb Ans: c) the unit vector in the…

A: As per our guidelines we need to solve only 3 subparts.please repost the remaining questions as…