Let u = (– 3, 5, 3), v = (4, –- 5, – 2), and w = (0, 5, – 3). Assume · always refers to the dot product. If possible, find the following. If not possible, type DNE. Use < and > to enclose vectors: for example, < x, y, z > u· v = (3u) · (4v) = (v. w w) u. (3v + 4w)

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 v = -2i + 5j, find a vector orthogonal to v.

A: Given v=-2i+5j We need to find a vector that is orthogonal to v. Two vectors are said to be…

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: Given vector u = (3, 1) and v (1,3) , determine the value of 2u – 3v in component form.

A: Use component wise addition and multiplication for required answer.

Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: If u is a vector and a is positive scalar satisfying   au+1,-2,5=0.  To find : a and u.

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. -2u

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Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

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Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: Given the vectors in parts a) and b), determine whether u, v, and w lie in the same plane when…

A: We have to determine whether vectors u, v and w lie in the same plane when positioned so that their…

Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

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Q: Find the vector v and illustrate the specified vector operations geometrically, where u = (−2, 3)…

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Q: Given the points M[0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector…

A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: A. Find the values of a such that vectors and are orthogonal .

A: According to bartleby expert policy only one individual question is to be answered. Kindly repost…

Q: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. Show that A x (B x…

A: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. To show :-A x (B x…

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

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

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Q: Which of the following is the correct value of the dot product for the vectors: u→=(6,−2,5) and…

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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 = 5u − 3v −…

A: Given: u=1,2,3, v=2,2,-1, w=4,0,-4 for finding given vector z, we use given values

Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out b) e1-e3

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Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Let u = (2, – 4) and v =(-4,2). Find the component form and magnitude (length) of the vector 2u -…

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Q: Determine if the given vectors are orthogonal. a. v = 3i – 6j and w = 8i + 4j b. s = -2i – 5j and r…

A: Consider the pair of vectors  a)v=3i−6jw=8i+4j b)s=−2i−5jr=−4i+8j

Q: Let v = -5i + 2j and w = 2i - 4j.Find the specified vector scalar, or angle 3v - 4w.

A: It is given that, v = -5i + 2j and w = 2i - 4j

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: Find the coordinate vector of w relative to the basis S = {u1, u2} for R2. : (6, – 6), u2 = (2, 2);…

A: Here we have to find the coordinate vector of w relative to the basis S ={u1,u2} for R2 . Here…

Q: If u, and uz are orthogonal unit vectors, and v = au, + bu2, find v•u . v•u1 II

A: topic - vectors

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 3u…

A: u=-3, 4 &amp; v=2, -5 a). 3u-4v=3-3, 4-42, -5=-9, 12-8, -20=-9-8, 12--20=-17, 32

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: Let v = -5i + 2j and w = 2i - 4j. Find the specified vector, scalar, or angle 3v - 4w.

A: Let v = -5i + 2j and w = 2i - 4j. Find the specified vector, scalar, or angle 3v - 4w.

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: ..) Find a vector ğ so that if F{f} = (co, C, C2, C3) then Ff ® ğ = (co, 0, 3c2, 0). %3D 160

A: The objective is to find the vector g so that is F(f)=(c0,c1,c2,c3) Then, Ff⊙g=(c0,0,3c2,0) It is…

Q: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

A: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: Let the two vectors be u=u1i+u2j+u3kv=v1i+v2j+v3k

Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: Find the magnitude and direction of the following vector products: (а) А(1, 3) х в(3, 1) (b) А(-1,2)…

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Q: Given vector u (-1, 5) and v = (5, 3) , determine the value of 2u – 2v in component form.

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

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Q: Find the vector z, given that u = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

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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 = &lt;1, 2,…

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: a a

A: For first figure. a→+a→+b→+d→-c→=02a→=-b→-d→+c→a→=-b→-d→+c→2    Answer

Q: Find the sauare of the magnitude of the vector w =u + 2v if u = (8, 2,0) and V = (-1, 1, 2) |wf =…

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Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: It is known that the unit vector along the direction v is given by vv. Since it is an unit vector,…

Q: Find a nonzero column vector u such that Cu = 4u.

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Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.