Question 6 Two vectors are orthogonal if their inner product is equal to 90. True False

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

A: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

Q: QUESTION 3 Consider the set of vectors S = {2 – x + 4x²,3 + 6x + 2x²,2 + 10x – 4x²} in P2. Show that…

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Q: Find the magnitude of the vector AB A=(-1,-1) and B=(2, - 5)

A: The coordinates of the vector AB are found by subtracting the coordinates of the initial point, A…

Q: C A

A: We use Triangle law

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

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Q: Show that the vectors below are independent. 1 3 3 3 5 3

A: The given vectors are 123,  -1-15   and  333. Compute the determinant of matrix formed by these…

Q: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

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Q: Question 6 Match each property of vectors with its name. 1. u+v=v+u for all vectors u, v e R"…

A: Associativity of vector addition : u+v+w =u+v+w for all vectors u,v,w∈ℝn. Commutativity of vector…

Q: Let a = (-1; 3; 2) and b = (4; -2; 1). Find two unit vectors orthogonal to both a and b. Are the…

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Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non-orthogonal because the dot…

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Q: Question 7. Show that if =0 and u - = 0, then i = 0. Let i, u be two linearly independent vectors in…

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Q: Question 1 For which are the vectors u = (a, 5, b) and v = (2, −2, 0) orthogonal

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Q: Are the following vectors linearly independent? ,, Do the following apply to give an answer? ?…

A: the given vectors,  4,0,0,, 5,-1,0,1,5,5

Q: Is it true that if vectors a-b and a+b are orthogonal, then |a|=|b|.

A: For orthogonal, dot product of two vector is zero

Q: 11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and v. u= (2,-1,3) v=(1,0,–2)…

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Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

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Q: Question 11. Let R³ have the Euclidean inner product, -1 2 and W = span{u1, U2}. Uj = U2 = v = %3D…

A: As you have asked three different questions(in terms of logic and answer of one are not required for…

Q: Two vectors are equivalent if they have the same _______ and _________.

A: Two vectors are equal if they have same magnitude and same direction. If we have a vector u=3i+4j…

Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given that : The statement : Given two nonzero vectors v and w, v can be decomposed into two…

Q: 3. Using the result form question 2 find the coordinates of vector w (1, 2, 3) in basis B.

A: 3)

Q: Question 3. Let v and w be vectors in inner product space V. Prove that v is orthogonal to w if and…

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Q: Question 31 2 1 1 U2 = 1 and W =Span{u1; U2, U3}. For 1 Let Uj = Uz = 1 1. 6. in W ? what value oft…

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Q: Question 11 A vector space may have two or more zero vectors. True O False

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Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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Q: Question 3. Let v and w be vectors in inner product space V. Prove that v is orthogonal to w if and…

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Q: Answer 19) (Section 9.7) Find a unit vector orthogonal to both vectors u = 2i +5 j–k v=i+3j-2k Tem…

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: 19) (Section 9.7) Find a unit vector orthogonal to both vectors u = 2i + 5 j –k v=i+3j-2k %3D…

A: We know that the cross product yields the vector orthogonal to both vectors .Here…

Q: Question 2: Prove the vector À = 3î + j – k is Perpendicular the vector B = î -2j +k

A: Given vectors are A=3i+j-k  and  B=i-2j+k.

Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Question 4: Find basis for R*, that contains the vectors vị 2 and 1 v2 = -1]

A: A basis to an n-dimensional space is a set of n vectors which span the space and are linearly…

Q: A, B and C are points in space relative to 0 such that AB 1 CO and AC 1 BO. Prove that BC 1 AO. The…

A: Given: A, B and C are points in space relative to O such that AB⊥CO and AC⊥BO. To show: BC⊥AO.…

Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: a-(:) We have two vectors: a = and b= What is the resultant of -a plus b? (

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Q: Question 3. Let V be a vector space and u, v, w its basis. Are the vectors {2u, u + 3v, –u +v – w}…

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Q: The number of elements in a vector generated by [4:0.1:13] is

A: We have to find the number of elements in a vector generated by  [4 : 0.1 : 13].

Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

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Q: Question 4: Find basis for R*, that contains the vectors vį = and V2 = -1] 1234

A: In the given question we have to find the basis of which contain the vectors . Concept: here we…

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

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Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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Q: Suppose that u and i are vectors in R and c is a scalar. Decide whether each statement is always…

A: Given data- We have given two vectors :u→ and v→ in R3  . we have given the four statement and we…