9. Use the cross product and determine the volume of the parallelepiped generated by the three vectors ā=(-1,4,4), b = (3,–3,2) and ĉ = (4,–2,7) [A:4]

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

A:

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: 11. Find the volume of the parallelepiped determined by the vectors u = 2i + 3j - k, i + j - 2k ,…

A:

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

A:

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

A:

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

A:

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

A:

Q: 12. Find the volume of the parallelepiped spanned by the vectors (1, 1, 2), (2,2, 1), and (0, –4,…

A: The given vectors 1,1,2, 2,2,1, 0,-4,0

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

A:

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

A:

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are…

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 = (6, 3, -2). b= (0,…

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

Q: ) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpe ular to CD, and…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

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

A:

Q: 5- Find the volume of the box (parallelepiped) determined by the vectors 0 = (0,0,0), B = (1,1,2)…

A:

Q: In Exercises 30–35 compute the indicated quantities when u = (−3, 1, −4), v = (2, 0, 5), and w =( 1,…

A: Given: u = (−3, 1, −4), v = (2, 0, 5), and w =( 1, 3, 13)

Q: 29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are,…

A:

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

A:

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: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

A:

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: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

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: Calculate the cross product assuming that u x w иxw3D (2, 6, 1)

A: Given vector u x w <2, 6, 1>

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: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

A: I am going to solve the given problem by using some simple algebra to get the required result.

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…

A:

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: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

A:

Q: Find the volume of the parallelepiped defined by the vectors 2 4 -4 -2 4 3.

A: We have to find volume

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: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

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

A:

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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: 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: 18. Calculate the volume of the of the parallelepiped spanned by the following vectors. Interpret…

A:

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 triple scalar product to find the volume of the parallelepiped having adjacent edges given…

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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=[…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

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

A: