Find the weighted Euclidean inner product (u, v) = -3v1 u1 – 3vzuz of the given vectors. u = (u, v) = Ex: 5 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 orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

A: In the given question we have to find the unit vector orthogonal to both u and v. u=8i-16j+2k…

Q: An inner product (•, ·) on R³ under which the vectors 1 Vị = 1 1 , V2 = 2 satisfy (v1, v2) = 0…

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Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: Consider (u, v) = 0 for any vectors u, v e R4. Is this an inner product? Explain why or why not.

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Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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Q: Find the Euclidean inner product of the given vectors. 3 4 u = v = (u, v) = Ex: 5

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Find the projection of u onto v and the vector component of u orthogonal to v for u = 3i − 5j + 2k…

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Q: Find a unit vector orthogonal to both u and v. u = 3i + 5j + 2k V= 위해 + -k 10

A: Given the vectors u→=3i→+5j→+2k→, v→=12i→-34j→+110k→. To find: A unit vector orthogonal to both u→…

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

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Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

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: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

A: Topic:- vector

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv of the given vectors and then we have to decompose v into two vectors, v1 and…

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: ^2

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Q: Find the weighted Euclidean inner product (u, v) = 2v1u1 – 4v2 U2 of the given vectors. 3 4 V = u =…

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Q: Given the vectors P=3i - j +k, Q =4i +Qy j-2k, and S=2i -2j +2k,determine the value of Qy for which…

A: given the three vectors P=3i-+j+k , Q=4i+Qyj-2k  and S=2i-2j+2k are coplanar vectors. we need to…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are coplanar

A: We have to determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are…

Q: For two-dimensional vectors u= and v= , then the dot product is simply the scalar obtained by ủ ·…

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Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

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

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Q: Find a set of vectors {u, v} in Rª that spans the solution set of the equations w – x + 2y – 4z 0,…

A: The detailed solution is given below Thank you

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: Let B = {v2, v2, . . . , Vk} be a set of orthonormal vectors, this is, vi vj 0 if i # j and v; · Vi…

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Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Let v = 2i + 4j and w = -2i + 6j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: v=2i+4j  &  w=-2i+6j Now, v·w=2-2+46=20 & w=-22+62=40 Now,…

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Consider the following. u--8i-4j-2k, v - 4j+4k (a) Find the projection of u onto v. (b) Find the…

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Q: Find a unit vector orthogonal to both u and v. u = 3i – 5j + 2k -k + 10 - V =

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Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with…

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Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: Find a unit vector orthogonal to both u and v. u = -3i + 5j + 2k V + 1k 10

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Q: In Rn with inner product{x, y} = xTyderive a formula for the distance between two vectorsx = (x1, .…

A: Take two vectors x and y in an inner product space x=x1,…,xn and y=y1,…,yn then x,y=xTy

Q: Find the Euclidean inner product of the given vectors. 4 5 u = 3 v = 1 -4. -2 (u, v) =Ex: 5

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