Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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Q: C A

A: We use Triangle law

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

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Q: Show that if u and v are orthogonal unit vectors then u x v is also a unit vector.

A: To show: That if u and v are orthogonal unit vector, then prove that u×v is also a unit vector:…

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Show which of the following are orthogonal vectors v, = 18] V2 = %3D Or = Liel Uz = 18

A: Check the dot product of given vectors are zero or not, if zero the orthogonal otherwise not

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Find the angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: For any vectors u, v and w, show that uxv=uxw does not always imply v = w. Prove that u v ≤ ulv, and…

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

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find Projwv and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is…

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Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: Prove that the vectors v= and w= are orthogonal.

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Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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Q: Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

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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 angle between the vectors u (2, –1) and v = (1, 1).

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Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: What is the resultant of vectors a and b? (

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Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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

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Q: Let u and v = .A vector orthogonal to both ú and v is

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Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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Q: Show that for any two vectors u and v: = |

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Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

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