Q5) Answer true or false for the followings: i) in triple dot of vectors |(A × B).C| = |(C × A). B|, where the vectors A,B , and C are not same plane. ii) in triple cross of vectors (A x C) × B = C × (B × A). iii) 12 = 1-2 ,where I is 2 x 2 unit matrix. iv) (x + yi)(3i + 2) = (2x – 3y) + (3x + 2y)i

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: نقطتان )2( The cross product of the vectors 3ax + 4ay - 5az and -ax + ay - * ,2az is -Зах -11ау -7az…

A: Dot product

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: Suppose u = (2, 3) and ī = (3, 11) are two vectors that form the sides of a parallelogram. Then the…

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Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

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Q: . For what values of c are the vectors [−8, c, 4] and [c, c^2, c] orthogonal?

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: 6. Consider the problem of determining whether the following system of equations is consistent: 14.…

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Q: For a C4 axis along z axis, please find the matrix for c, the synmetry opertion on a vector·

A: Given, C4 axis is along z axis . Upon action of C14 symmetry operation, the change with respect to x…

Q: 7. Find a 2 x 2 matrix that reflects vectors in the (x, y) plane across the x axis. 8. Find a 2× 2…

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: 2. (а) Find all unit vectors orthogonal to both u = 2i – 3j + k, v = -3i + 3j + 2k If a, b, and c +…

A: In the question it is provided two vectors: u=2i-3j+k and v=-3i+3j+2k The objective is to find all…

Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

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Q: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: 2- Concisely describe what the following terms mean for a set of vectors and how we quickly check…

A: Define: 1. Collinear vectors 2. Coplanar vectors 3. Linearly independent vectors 4. Linearly…

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: Please reply as soon as posible Consider the vectors u = (1, -8,5) and v = (- 15.0, -3) The vector…

A: Given vectors are u = (1, -8,5) and v = (- 15.0, -3)

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: Can you find two vectors in R whose dot product is equal to their cross product? No, because the…

A: (iii) can you find two vectors in ℝ3whose dot product is equal to its cross product as we know , dot…

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Two vectors u and v are said to be orthogonal if u·v=0. Given that, u=1-12 and v=k2k-3 We have to…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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

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Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: TRUE/FALSE If x and y are nonzero vectors in Rn and A = xyT , then the row echelon form of A will…

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Q: Find the area of the parallelogram defined by the vectors ä= (2, -2,0) and 6= (0,1,2)

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: In Cartesian coordinates, a rank-2 tensor is given by Į = Tr£xx + Tvz£xz+ Tyy£yy and a Cartesian…

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Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

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