1. Let u = PQ and v = PR, where P = (2, –1,3), Q = (0,5, 1), and R = (5,5, %3D (a) u v (b) The angle between u and v (c) projuv (d) ux v (e) The area of the triangle that has u and v as adjacent sides (f) A unit vector that is orthogonal to both u and v

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: Find x∈R such that vectors a = and ?=. are equivalent

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Q: Let u =(0,1,2) and v=(-2,2,0). Find %3D a. A vector w orthogonal to both u and v. b. The area of the…

A: The orthogonal vector both u and v is u×v . And the area of parallelogram is |u×v|

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

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Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Let u = (2, −1, −1) and v = (5, -3, 3). A vector with integer components perpendicular to ū and v is…

A: <-6, -11, -1>Explanation:Step 1: Determine how to find the perpendicular vector To find a…

Q: Let P be the point (1, –3, 0) and ū be the vector ī = (-3, 6, 2) %3D • Find the point 1 unit away…

A: Given: The point P=(1,-3,0) and the vector v→=-3,6,2

Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: Let u=i-3j+2k, v=i+j, and w=2i+2j-4k be vectors in 3-space. Find: (a) ||u+v (b) unit vector in the…

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Q: Find the angle 0 between the two vectors u = and v = .

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