02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8, -4) is equal to zero. Explain why?

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: 2. Find the volume of the parallelepiped having a = (1,4,–7), b = (2,–1,4) and c = (0,-9,18) as…

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Q: Show that the lines L1 : x = 4 – t, y= 2t, z = 5+t and L2 : x = 1+4t, y= 3 – 8t, z= 5 – 4t are…

A: Let's find.

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: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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

A: Solution

Q: 2. Find the volume of the parallelepiped formed by vectors d (-1, 2, 1), 6 = (3, –2, – 1) and T =…

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Q: Find the volume of the parallelepiped determined by the vectors u = (1,2,-3), v = (2,4,-1), and w=…

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Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

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Q: Find the volume of the parallelepiped determined by the vectors = (1, 2, 3), b = (3, 0, 6) and c =…

A: This question is related to vectors, we will solve it by using the formula of volume of…

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: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. а 3 (6, 2, -2), ь 3 (о,…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine…

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: To find:- volume of the tetrahedron with vertices P(-4, 4, 0), Q(2, 1, -3), R(1, 0, 1) and…

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

A: Given: The expression for the volume of tetrahedron is: V=16u·v×w And The vertices P-2,5,0, Q2,1,-3,…

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

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

A: Volume of a tetrahedron with adjacent edges given by the vectors u,v,w is given by, V= |u.(v×w)|/6

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

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

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Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c.  a = 1, 2, 2, b = −1,…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (4, 2, -2), b = 3…

A: Given:- a = (4, 2,-2), b = (0, 2, 1), c = (4, -3, 4) To find :- Volume of Parallelepiped

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ‹6, 2, -1›,     b…

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

A: We will use the given formula of volume to find the volume of the tetrahedron.

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: Find the volume of the parallelepiped defined by the vectors 5 5 5 ne =

A: To find: The volume of parallelepiped defined by three vectors 0-15, 55-3 and 5-4-2. Concept used:…

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 2, 3), b = (-1,…

A: Given vectors:                        a=1, 2 , 3, b= -1, 1, 4, c=5, 1, 5

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

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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

A: To find out the volume of the tetrahedron whose vertices are given.

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 3, 3), b = (-1,…

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

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: This is the problem of vector algebra.

Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: 9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4] [- 2,9, 1] w = [0, – 4,…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: 9. Use the cross product and determine the volume of the parallelepiped generated by the three…

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Q: 6-Determine the volume of the parallelepiped formed by the vectors U= [2,1,3], v= [1, -4,2] and w=[…

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