9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4]v = [-2,9, 1] w = [0, – 4, – 7] | |

Q: 4 4. Let S be the parallelepiped determined by the vectors p, = 0, P2 =5 and 3. 2 3 -3 0 P3 =0 and…

A: Solution of given problem is as below:

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

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Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

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: 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: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: 3. (а) Consider the vectors ū = i – 6j + 4k, ở = 2i – 5j – 3k and w = 6i – 2j + 3k Show that ū x (T…

A: Use the formula for determining the cross product of two vectors  Substitute the values given and…

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: If v = (1,2 ) draw all vectors w = (x, y) in the xy plane with v · w = x+ 2 y = 5. Why do those w's…

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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: 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: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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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: 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: 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 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: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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

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Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

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Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

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

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Q: 2. Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 2, (v, w) = -6,…

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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: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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: 10. Find the volume of the box generated by the vectors i, j+ k, and i+ 2j + k.

A:

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

A: Given are the vectors  a= (3, -1, 1), b= (4,0,2) and c= (-1,-2,-3) The objective is to find the…

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

A: Find your answer below

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1.3,4). b =…

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Q: The dimension of the vector space P; is equal to: Select one: O 5 none of the others 4

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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:

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 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: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

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: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

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: Suppose that u, u and w are vectors in a real inner product space such that (u, w) = 16, (v, w) = 5,…

A: Instead of u¯,v¯,w¯ , we are writing u,v,w. (for sake of convenience). Given: (i) <u,w>=16(ii)…

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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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 1 by the vectors u, v and w…

A: Solution is given below: