Q3/ Determine whether the given vectors are orthogonal, parallel or neither: (1) u =(-2, 6, -4) , v = (4 ,-12 , 8) (2) u= (2, 6, 3) , v= (4, -1, -3)

Q: The component of the vector (-5, 0, –3) onto the vector (3, –4, –2).

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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: How to calculate the cross products of vectors ? = {3,4,7} and ? = {4,9,2}?

A: GIVEN: Two vectors {3, 4, 7} and {4, 9, 2}

Q: What is meant by the term translation in vectors?

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Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0). (smaller i-value) (larger…

A: Consider the given vectors. Cross product of two vectors is perpendicular to both the vectors. This…

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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Q: Find two unit vectors orthogonal to both (2, 7, 1) and (-1, 1, 0). (smaller i-value) (larger…

A: Given that the vectors are 2,7,1 and -1,1,0.It is required to find the two unit vectors orthogonal…

Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Find two vectors v¯¯¯1v¯1 and v¯¯¯2v¯2 whose sum is ⟨2,−4⟩⟨2,−4⟩, where v¯¯¯1v¯1 is parallel to…

A: Given, v1+v2=2, -4v1 is parallel to 2, -4v2 is perpendicular to 2, -4. if two vectors a and b are…

Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

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: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

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

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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

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

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

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

A: The given vectors are u=(0,1,1) & v=(1,0,1).

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

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Q: Find four different nonzero vectors that are orthogonal to v = (-1,5,2)

A: This is a simple problem based on orthogonal vector which could be solved by using basic knowledge…

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: The cross product of vectors a = (-1, 4, 6) and b = (3, 0, -2) is %3D

A: The cross product of vectors is given below

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: Find the area of the parallelogram that has the given vectors u = ⟨2, −1, 0⟩,     v = ⟨−1, 2, 0⟩ as…

A: Given vectors as adjacent sides are u=2,-1,0, v=-1,2,0.

Q: Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

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Q: Find two unit vectors orthogonal to both (5, 8, 1) and (-1, 1, 0). (smaller i-value) (larger…

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Q: 2. Write the vector v = (1,3,2) as a linear combination of vectors u = (1,2,1), %3D (2,6,5), uz =…

A: We have to write a vector v to a linear combination of the vectors u1, u2, u3

Q: Find two unit vectors orthogonal to a=⟨1,−1,−2⟩a=⟨1,−1,−2⟩ and b=⟨2,0,−2⟩b=⟨2,0,−2⟩.

A: Given vectors are

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

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Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

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: The independent vectors are also orthogonal. Select one: True or False

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Q: Determine which vectors that are orthogonal to (– 3, -6)? (-4,2) and (-1,3) (-10, 5) and (-3, 6) a.…

A: To determine the vectors which are orthogonal to -3,-6. (a) Given vectors are -4,2 and -1,3. We know…

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

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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: What helps to set of vectors linearly independent?

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

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

A: We will solve the problem

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: Let u, = (1,1,1)", u2 = (1,2,2)T and uz = (2,3,4)", find the coordinates of the vectors (2,3,2)" and…

A: Solving by linear combination method

Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

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: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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

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Q: )Find the vector in R2 from point A = (8,9) to B = (-3,5). AB = help (vectors)

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Q: The vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

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