Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

Q: Let V be the set of vectors shown below. V= x> 0, y>0 a. If u and v are in V, is u +v in V? Why? b.…

A: Please check step 2 for solution.

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

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Q: Let v be the vector from initial point P1 = (3, -1) to terminal point P2 = (-2, 5).Write v in terms…

A: Given the points P1=3,-1 and P2=-2,5.   The vector is, v=P1P2→=-2-3,5--1=-5,6

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

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

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: Let v be the vector from initial point P1 = (-1, 3) to terminal point P2 = (2, 7). Write v in terms…

A: Given : the two points are given as P1=-1,3 and P2=2,7 To find: a vector v from initial point P1 to…

Q: а — Ь Let W be the set of all vectors of the form Find vectors i and v in R' such that W span {u,…

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Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: et u (x, y) E R² any vector, prove that l|u||

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Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Let F = 3 x R, where is a constant vector. Calculate F. dR C on the line segment C connecting (1, 3,…

A: According to the given information, it is required to calculate the integral.

Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

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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: 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: 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: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Write w as the sum of a vector in Span{v} and a vector orthogonal to

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Q: Let x and y be two orthogonal vectors. Then prove that +

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Compute the curl of the following vector V defined by V(x,y,z) = e(x²+y² +z²) y

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Q: Let V be a Pinite-diemeniond Vector

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Q: Determine whether or not the vector ficld F (r, y, z) = (2ry22, 3ry2, 2ryz) is conservative. If it…

A: The general form of a vector-valued function in three dimensions is given by F=F1,F2,F3, where F1,…

Q: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

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: Let u= and w- Find the unique vector v in R'such that u.v 1, v is orthogonal to w, l|v|| V3, and y>…

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: Find the vector projection of vector u onto vector v, and find the vector component of u orthogonal…

A: The projection of vector u onto v is given by projvu=u⇀v⇀v⇀2v⇀

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

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: Find a unit vector orthogonal to both u and v.u = 3i + j v = j + k

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Q: Determine the constant a so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal.

A: Follow the procedure given below.

Q: Find a non-zero vector u perpendicular to the vector u =

A: If  A non zero vector is perpendicular to anather vector then their dot product is equal to zero.

Q: Linear algebra

A: From the given information:Let,

Q: Let y = 185 || 3 and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: Let T R2 R2 be a linear transfor [3] into the vector a (i) T maps vector u

A: Introduction: A linear transformation could be a operation from one vector area to a different one…

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: Let r (t) = |r (t)| = ( the length of the vector is round to one decimal

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