Determine the volume of the parallelepiped formed by the vectors P = (2,4,3), Q = (1,3,2) and R= (4,3,–1).

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

A:

Q: What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v, and w?…

A: A prism, made of parallelograms; a polyhedron with six faces, each of which is a parallelogram.  The…

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

A:

Q: Determine the volume of the box whose sides are the vectors (1, -2, 1), (2, 3, -2), (-1, 3, -2)

A: use determinant method to findout the volume.

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

A:

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

A:

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

A: Given problem:- Determine the volume of the tetrahedron with vertices P(-4,4,0), Q(2,1,-3), R(1, 0,…

Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: Compute the volume of the parallelepiped dened by the vectors v1 = (1, 3, 1), v2 = (2, 1, -1) and…

A:

Q: Find the volume of the parallelepiped determined by the vectors å = (3, 4, – 1), 6 = (0, 2, 1), c =…

A: The volume of the parallelepiped  determined by the vectors a, b and c is given by a·b×c or…

Q: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

A:

Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

A:

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

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

A: To find the volume of the tetrahedron whose vertices P , Q , R and S are given .

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

A:

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, –…

A:

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: What is the area of the parallelogram determined by the vectors v = (1, 3, 6) and w = (-1,0, 3)?

A:

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

A:

Q: Find the volume of the parallelepiped defined by the vectors й%3 (3, —1,4), ѣ —D (2, 1, —2) and й %3…

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

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

A:

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: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

A:

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A:

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

A:

Q: 5) Find the volume of the parallelepiped defined by vectors u = [1, -3, 6], v[-2, 5, 6] & w = [1, 2,…

A: Calculating the volume of parallelepiped

Q: Compute the volume of the parallelepiped defined by the vectors vị = (1,3, 1), v2 = (2, 1, – 1) and…

A: Given that three sides of the parallelepiped are: v1 = (1,3,1) , v2=(2,1,-1) , v3=(1,0,1) So the…

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: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

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

A:

Q: Compute the volume of the parallelepiped defined by the vectors vi and v3 = (1,0, 1). (1, 3, 1), v½…

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

A:

Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

A:

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

A:

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

A:

Q: Find the area of the parallelogram spanned by the following vectors. u = [4, –6, 5] v = [0, 6, 8]…

A:

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

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

A:

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

A:

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

A:

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

A:

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

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: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.