The area of the parallelogram with vectors R(1,2,-1), P2(4,2,-3), P3(6,-5,2).P4(9,-5,0) is a) 998 b) 899 c) 1998 d) 998 e) 989

Q: Find the volume of the parallelepiped determined by the vectors c č = (2, 4, 1). %3D

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Q: Find the of A ABC Where the area vectors AC1,-1,1), B(2,1,1) and are cl-1,1, 2).

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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,…

A: Please refer the attached image for complete solution.

Q: Find the volume of the parallelepiped determined by the vectors a = (5, 2, – 1), b = (0, 4, 1), č =…

A: We will find the volume of the parallelepiped by using the given vectors.

Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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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: ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA  respectively and are…

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Q: Find the volume of the parallelepiped with sides give by the three vectors a = 2i – 2j+ 3k, b = 5i+…

A: a→ = 2i^ -2j^ +3k^b→ = 5i^ +2j^ +6k^c→ =-3i^ +2j^ -2k^Volume of parallellpiped = a.(bx c¯

Q: Find the volume of the parallelepiped determined by the vectors a = (3, 4, – 1), b = (0, 4, 2), с 3…

A: Given the vectors, a→=3,4,-1b→=0,4,2c→=2,5,1

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: Prove the stated property of distance between vectors. d(u, w) <= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č =…

A: Given query is to find the volume of the parallelopiped.

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

A: The volume is given by scalar triple product of vectors. a→=4,2,-1, b→=0,3,2,c→=2,3,1

Q: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

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Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

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

A: The volume Parallelepiped by the vector a, b and c is given as:

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: 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 volume of the parallelepiped determined by the vectors a = (2, 3, – 1), 6 = (0, 2, 1), c=…

A:

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

A:

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

A: Find the solution below

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

A: Known facts: The area of the parallelogram that has the given vectors u  and v as adjacent sides is…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 2, 4   b = −1,…

A: First find cross product of b and c and take dot product with a

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: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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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 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: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

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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: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: 2. Determine the volume of the parallelepiped formed by the following vectors (a) ā = (2, –6, 2), 5=…

A: To findvolume of parallelpipedmethod:volume of  parallelpiped=a→b→c→a→b→c→=a1a2a3b1b2b3c1c2c3here…

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: Find the volume of the parallelepiped determined by the following vectors. a) u = (3,2,8), v = (5,…

A: Find your answer below

Q: Prove the stated property of distance between vectors.d(u, w) < d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

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: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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

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Q: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

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Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

A: The given vectors are a=8,1,0, b=1,4,1 and c=1,1,10

Q: Find the signed volume of the slanted box in R“ generated by the vectors 27 11 11 -2 3 , U2 = V3 =…

A: Form a matrix of the given vectors, A=v1v2v3v4=0-2-1-12-1-236-10-23030 The volume of the slanted box…

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

A: answer is following-

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: Consider the quadrilateral (four-sided plane figure) formed by the points P(3,3, 2), Q(3, 4, 3),…

A: Area of parallelogram ,A =u×w