Perform the following operations on the vectors ū = (5, –2, 1), v = (-1, –2,0), and (3, 3, –4). w = ((w.w)ū) · ū ||

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩     (1/3)z − 3u = w

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Q: If S is a function of (x, y, z) coordinates, and P = Ai - Bj - Ck where i, j, and k are the unit…

A: S is the function of (x,y,z) and P→=A i-B j-C k i, j, k are unit vectors. Solution 1: ∇×∇·∇S Since…

Q: Perform the following operations on the vectors u = (1, 3) and v = = (-3,4) %3D a. v b. u · v C.…

A: Please see the answer below.

Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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Q: photo attached

A: Given informationU=(4, 1),  V = (-7, 3)That is U= 4i+1j      V = -7i+3j

Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

Q: For the following pair of vectors, find U · V. U = 6i + 7j, V = 7i + 6j

A: This question is based on Dot product.

Q: The figure shows two vectors in the xy-plane with |u| = 3 and v = 4 Which of the following could be…

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Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: Which of the following vectors are equal to j × i? i × j

A: The standard unit vectors in three dimensions, i^, j^, and k^ are length one vectors that point…

Q: Without doing any calculations, explain why the following sets of vectors are linearly dependent:…

A: Since you have posted multiple question with multi part we are supposed to give solution of first…

Q: Find the coordinate vector of w relative to the basis S = {u1, u2 } for R2 u1 = (9, – 9), uz = (3,…

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Q: photo attached

A: Given vectors are

Q: For the following pair of vectors, find U · v. U = -11i + 5j, V = 9i – 3j

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Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Perform the following operations on the vectors u = (1, 3) and v = -3,4, a. |v| b. u· v c. Angle…

A: We can answer all the three questions as below.

Q: find II u II for the given exercise, and give a unit vector in the direction of u.

A: Given a vectors

Q: For the pair of vectors, find U + V, U – V, and 4U + 3V. U = 2i + 7j, V = 7i + 2j U + V = U - V = 4U…

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Q: Perform the following operations on the vectors u = (1, 3) and v = (-3,4) a. v| b. u· v C. Angle…

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: Determine all vectors v that are orthogonal to u. (Set v, = t and v3 = s and solve for v2 in terms…

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Q: Find the vectors T, N, B at the given point where 0sts 2n. (1 3/3 8' r(t) =

A: We want to find the unit tangent vector , normal vector and Binormal vector

Q: Show all work to calculate the value of x that makes the two vectors orthogonal to each other. v =…

A: Orthogonal vectors: Two vectors a→ &  b→ are said to be orthogonal if they are perpendicular to…

Q: Perform the following operations on the vectors i = (-5, 3, –2), i = (4, 5, 0), and w = (-1, –5,…

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Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: Which of the following vectors are equal to j × i?(a) i × k

A: We know that, i×j=k Therefore, j×i=-k Hence the answer.

Q: For the following pair of vectors, find U · V. U = 6i + 2j, V = −6i + 2j

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Q: Which of the following vectors are equal to j × i?(a) i × k(b) −k(c) i × j

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Q: Find the cross products U * V and V * U for the vectors U= 3i-j-2k and v=i+3j-2k U*V = ?i +?j+?k…

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Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: Find the component form of the vector v given ||v|| 12 following the direction of u (3, –5) %3D

A: The vector v in direction of u can be found  blew step.

Q: For the following pair of vectors, find U · V. U = −7i, V = 9j

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Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: find ||u|| for the given exercise, and give a unit vector in the direction of u.

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Q: For the pair of vectors, find U + V, U - v, and 2U – 3V. U = (-3, 0), V = (0, 2) U + V = U - V = 20…

A: Given vectors are Sum of vectors  u and v is Difference of vectors u and v is

Q: Find the values of x such that the vectors (4x, , 3) and (2,x,5) are orthogonal. Select all that…

A: Find the value s of x for which the vectors are orthogonal

Q: For the following pair of vectors, find U · V. U = −2i, V = 9j

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Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: find ||u|| for the given exercise, and give a unit vector in the direction of u.

A: To find: Unit vector in the direction of u=3.2-0.6-1.4. Concept used: The unit vector in the…

Q: Find the vectors T, N, and B at the given point. r(t) =< t2 ,(2/3)t3 ,t>   ,  (4,16/3 ,2)

A: Consider the given vector function.

Q: Perform the following operations on the vectors (3, 2, −4), v = (-1, 5, −2), and = (0, 4, 2). ū = ū.…

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Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Find the following for the vectors u = - 9 i-2j + v2 k and v = 9 i+2 j- v2 k. a. v•u, v|, and u b.…

A: Let a→ = a1i^ + b1j^ + c1k^ and b→ = a2i^ + b2j^ + c2k^ two vector. Then, a.b = a1a2 + b1b2+c1c2 a…

Q: For this question, define the vectors v and w .

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Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Find the vectors T, N, and B at the given point. r(t)= (t2)i+(2/3(t3)) j + (t)k, (1,-2/3,-1)

A: Given, rt=t2i+23t3j+tk Point - 1, -23, -1 So, t=-1 Formula Used: Tt=r'tr'tNt=T'tT'tBt=Tt×Nt Quotient…

Q: find the derivitive, r'(t), of the vector function.  r(t)=a+3tb+t^7c

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