Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Prove that llu - vll >=llull -llvll for all vectors u and v in Rn.

A: According to the given information, it is required to prove the inequality.

Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: 23. Show that u + v < u + v for any vectors u and v.

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Q: Describe the​ statement, "A vector orthogonal to u and v​," using dot product and cross product…

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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: Show that span(u, v) = span(u, u + v) for any vectors u and v.

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Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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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: snip1

A: orthogonal to u means the dot product of the vectors should be zeroso v.u=0xy.31=03x+y=0from here we…

Q: The cross product of two vectors in R yields a scalar. True False

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: find the diJ tance betueen the vectors

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Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, −1, 0), v = (0, 1, −1)

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Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

A: Let us assume that u,v, and w are nonzero vectors.  The dot product of the vector of the scalar…

Q: Which vector in two-dimensional space has no corresponding unit vector?

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Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Are the follovwing vectors linearly independent? ,,

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: Show that the vectors , and are coplanar.

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Q: Exercise 4. Is it possible to have nonzero vectors u, v in V with uv = 0? Why or why not? (Here the…

A: Given: 4) V is a subset of vectors in Hamilton's quaternions. To explain: Why or why not there are…

Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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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: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

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Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

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Q: Let W Span{u1, u2, u3}. Write y as a sum of a vector in W and a vector orthogonal to W. %3D

A: Orthogonal Decomposition theorem: Let W be a subspace of ℝn. Then each y∈ℝn can be written as,…

Q: What helps to set of vectors linearly independent?

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Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: 3. Determine if the vectors linearly independent or linearly dependent Please explain your answer…

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Q: Explain the Combination of basis vectors.

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Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

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: For the vectors u = (-4,1) and v = (-2,3), calculate projyu and scal, u. projyu = OD

A: Here I am attaching image so that you understand each and every step.

Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

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