Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b? Moreover, is it possible that ~a •^b = 0 as well? Explain why or why not.

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

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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: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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Q: Find linearly independent vectors which generate al lutions of Ax = 0.

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Q: Find area of triangle whose vectors Р (3,3, 1), Р2-1,0,2), Р3(2,3,3)

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Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

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Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

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Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0)

A: The given vectors are The unit vectors can be obtained by the formula Now, find the cross product…

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

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

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

A: Solved below

Q: Find a vector that has the same direction as [4, 2,5] but has length 35.

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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: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: Express the product Ax as a linear combination of the column vectors of A. 2 3][3 -4 + 2 3 5 + 3 |…

A: To find out the correct option.

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

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Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

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Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

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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: Find a vector in the same direction as (3, –2) with length 10.

A: The vector that has the same direction as 3,-2 has the coordinates proportional to the given vector.…

Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as <-4, 6, 4> but has length 6

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

A: The vectors 3,2,1 and -1,1,0

Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-<u2,…

Q: Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle…

A: The vertices of the triangle is A7,4,-4, B1,-1,1 and C-8,-1,3

Q: Are the follovwing vectors linearly independent? ,,

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Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0).

A: Unit Vectors orthogonal to vectors  <2,3,1> and <-1,1,0>…

Q: Find the sum of the vectors (3,0,1) and (0,8, 0) and illustrate geometrically.

A: Solved below

Q: find two unit vectors orthogonal to (5,-5,3) and (-3,5,2)

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Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in…

A: Given that, v is a nonzero position vector in xyz-space.

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: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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Q: The dot product of two vectors is a ________ quantity. For this reason, it is some-times called the…

A: Let A and B be two vectors, the dot product is defined asA.B=ABcosθ, where θ is the angle between…