Show that the following vectors of v,(R) are LI : a, = (1, 1, 0); a, = (1, 1, 1); a, = (2, 1,3)

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

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Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: Show that the vectors below are independent. 1 3 3 3 5 3

A: The given vectors are 123,  -1-15   and  333. Compute the determinant of matrix formed by these…

Q: Are the following vectors linearly independent? Yes No , ,,

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Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Determine all vectors v that are orthogonal to u.u = (2, −1, 1, 2)

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Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: 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, 1,0,…

A: We know four vectors v1 , v2 , v3 and v4 in ℝ4  will be linearly independent iff , av1→ + bv2→ +…

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 a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

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: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

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

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Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

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: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

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 three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=<1,1,1> The second case we can take b=<0,1,-1> The…

Q: orthogonal to the vectors

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

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: 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 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: 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: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

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Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector