Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are orthogonal to each other.

Q: Find the vector z, given that u = (3, -2, 5), v = (0, 2, 1), and w = Z= z = −u + 4v + 1 _W 2 (-6,…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = (2, 0,…

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Q: Given the vectors ū = (-2, 1, 1) and V = (3, –1, 1), calculate the vector projection of ū onto V

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Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: Let u= (1,1,−2) and v= (a,−1,2). For what values of a are u and v orthogonal?

A: Two vectors are said to be orthogonal to each other if their dot product is zero. we are given u=…

Q: Determine all vectors v that are orthogonal to u.u = (0, −4, 3)

A: Given u=(0,-4, 3)we have to find all vectors v that are orthogonal to u,If u.v =0 then vectors u and…

Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: (b) For any arbitrary vectors u, v and w, prove that (u x v) x w = u x (v x w) if and only if (u x…

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

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: Find the weighted Euclidean inner product (u, v) = -3v1 u1 – 3vzuz of the given vectors. u = (u, v)…

A: Given u, v=-3v1u1-3v2u2 u=-3-2, v=14

Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

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Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)

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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 x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, −1, 1), v = (0, 1, 1)

A: Cross product is,

Q: Prove that u × v is orthogonal to both u and v.

A: Consider the two vectors u and v, Evaluate the cross product of the two vectors u and v,

Q: Let u = (−1, 1), v = (0, 1),and w = (3, 4). Find the vector x that satisfies u−2x = x−w + 3v.

A: u=-1, 1,  v=0, 1  &  w=3, 4

Q: Find u × v and show that it is orthogonal to both u and v.u = (−1, 1, 2), v = (0, 1, −1)

A: Given vectors

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)

A: We have given; u = (1, 1, 0), v = (0, 3, 0)

Q: Suppose u, v, and w are vectors in an inner product space such that (u, v) = 1, (v, w) = 0, (u, w) =…

A: Use the values given above for substitution after simplifying the problem.

Q: Compute the component of u along v. u =〈3, 2, 1〉 v =〈1, 0, 1〉

A: Given the vectors are u=<3,2,1> and <1,0,1>.Our Aim is to compute the component of u…

Q: Suppose u, v, w are linearly independent vectors. Prove that S is linearly independent where (a) S=…

A: A set of vectors v1 , v2 , v3 ,...,vk from a vector space V  is said to be linearly independent , if…

Q: Let u = (1, 3), v = (2, 1), w = (4,−1). Find the vector x that satisfies 2u −v + x = 7x + w.

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Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: compute the component of u along v. u = (3, 0, 9), v = (1, 2, 2)

A: the given vectors are: u=3,0,9v=1,2,2 we have to compute the component of u along v.

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

A: Now let

Q: Let u¯¯¯=⟨−3,−5⟩, v¯¯¯=⟨2,−2⟩, and w¯¯¯¯=⟨2,4⟩. Find the vector x¯¯¯ that satisfies 9u−v+x=2x+w

A: Given that: u=-3, -5v=2, -2w=2, 4

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: Show that if u is a vector in R2 or R3, then u + (−1)u = 0.

A: The objective is to show that if u is a vector in R2 or R3 then u + (−1)u = 0. Suppose u and O is a…

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

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Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: The vector v, is in Span{ v2,., Um } if and only if ( v1,., Vm ) are linearly dependent. O True O…

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Q: Let u = (1,2, –1,5), v = (0, 1, 1,0,) and w = (3, 4, –2, 15). Show that u , v and w are linearly…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = (1, 2,…

A: Using the graphing utility, w = u × v = (1, 2, −1) x (2, 1, 2) = (5, -4, -3)

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 a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: Show that if u is a vector in R2 or R3, then u + 0 = u.

A: To show that if u is a vector in R2 or R3, then u + 0 = u.

Q: Consider the sets of vectors  S={u,v,w} and T={u,v,w,x}. Which of the following is true:  -If T is…

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Q: For any vectors U, V and scalars a, b, prove that (aU) x (6V) = ab(U × V) (a) (b) (aU) - (bV) = ab(U…

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

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Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

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Q: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

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Q: If in R a vector u is orthogonal to vectors v and w, then { u, v, w} is an orthogonal set. True…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: Find the vector z, given that u = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

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Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…