Find a representation of the vector AB = (1,9,2) in R' by giving appropriate values for the points A and B such that neither A nor B is the origin. A = help (points) B = help (points)

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

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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.…

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Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: The vector (-1, 5, 3) is orthogonal to vector : Select one: О а. (0, 1, -2) O b. (-1, 1, -2) О с.…

A: Two non-zero vectors are orthogonal to each other if their dot product is equal to zero.

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 a unit vector orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

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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 the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

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Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: Find a unit vector that is orthogonal to both u = (- 1, 4, – 5) and v = (0,4,–7). %3D

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: How do you find out the projection of a vector u on a vector w

A: Projection of vector u on w is nothing but the dot product of u and w divided by magnitude of vector…

Q: Calculate a projection of vector B on A and prophecy of vector A on B. A = 4i - 3j + 2k.     B = 3i…

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

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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: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

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Q: Describe all vectors v that are orthogonal to u

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

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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: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: Find the scalar and vector projections of b onto a, where a = (-1,1,2) and b = (-4,5,8).

A: The solution of the problem is given in the next step.

Q: orthogonal to the vectors

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Q: Let u = (-3, -1, 3) and : = (3, 1, 2). Find the vector component of u orthogonal to a. a 3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: a' and b Expess the Vector paduct in from of de terminant: 2 = (2, a, as) 5= of where , (6, b, bs)…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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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: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

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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: Compute the projection of →a→ onto →b→ and the vector component of →a→ orthogonal to →b→. Let…

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Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

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: 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 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: Identify the vectors that are orthogonal to v = (1,2, 1) but not to w = (1,0, – 1). 口(-2,2,0) (-1,…

A: u and v orthogonal if u.v=0 i.e. let u=(x1,y1,z1) and v=(x2,y2,z2) then u.v = (x1 * x2)+(y1 *…

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

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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

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