Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2), w=(3,2,5,4). (Hint: The unknown vector should have dot product with all three vectors equal to 0. Also, = x,+x,' +x,'+x, =1)

Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

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Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

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Q: v, =,v, =, v, =

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Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

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Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

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Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

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Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

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Q: (2,1, –4,0), v = (-1,-1,2,2), and 19. Find two vectors of norm 1 that are orthogonal to the vectors…

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Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O

A: I have append the formula in solution part

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: Please reply as soon as posible Consider the vectors u = (1, -8,5) and v = (- 15.0, -3) The vector…

A: Given vectors are u = (1, -8,5) and v = (- 15.0, -3)

Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: 1. The vector in the opposite direction to u = (-1,0) and of half its length is 2. The vector of…

A: 1.The vector is u=&lt;-1,0&gt;2.The vector is v=&lt;-4,5,-3&gt;

Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

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Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

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Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

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Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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Q: Consider the set of vectors S = {u= (-1, 2, – 1), v= (2, – 5, 0), w= (1, – 3, – 1)}, then find the…

A: u=-1, 2, -1,  v=2, -5, 0  &amp;  w=1, -3, -1. Now, u·v=-12+2-5+-10=-12 u·w=-11+2-3+-1-1=-6…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

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Q: Find a vector ~v ∈ R^3 such that ~v is orthogonal to the vectors (2, 3, −1) and (1, −2, 3) and ~v ·…

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Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

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Q: Let v, ..., v, be vectors, and suppose that a point mass of m,..., m, is located at the tip of each…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O

A: