● Let u = 2-25 - 2k + ● and = 2î - 2Ĵ+k. Find a vector w such that the parallelepiped spanned by u, V and w is a cube. What is the volume of this cube? What is the volume of parallel piped spanned by the vectors ū, ū+v, and ů. V + W? +

Q: Find the area of the parallelogram that has the given vectors u = i + j + k,      v = j + k as…

A: Given: Vectors are u→=i^+j^+k^ and v→=j^+k^. To Find: Area of the parallelogram and use a graphing…

Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: The scalar triple product of three vectors gives the volume of the three-dimensional parallelepiped…

A: The Volume of the three - dimensional parallelepiped descrived by the vectors  is the scalar tripple…

Q: Find the volume of the parallelepiped defined by the vectors 37 2 1 2 3.

A: Introduction: The volume of parallelepiped that defines by the vectors a, b, and c is given by,…

Q: Find the volume of the parallelepiped determined by the vectors a č = (2, 4, 1). (3, 5, – 1), 6 =…

A: The volume, V , of a parallelepiped is calculated using the scalar triple product, V=c·(a×b) . Use…

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: 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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Q: can you add 3 vectors using the parallelogram method? support you answer

A: Parallelogram law : if two vector quantity are represented by the two adjacent side of a…

Q: det pC-1,2,-1) and Q(2,-7,8) be two points in three dimenonal space. Use vectors to fird the points…

A: Vector form of a point: Let (a, b, c) are any point in 3D- space. Then this point can be expressed…

Q: Consider the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1) Find AB and AD,…

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Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Suppose that a parallelogram is bounded at one vertex by the vectors i = |,3 = ,: Find the area of…

A: Area of parallelogram =|u×v| ,where u and v are the vectors which represent the side of…

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