Let A, B, C be points in 3-space. Suppose that AB represents u, BC represents v, AC represents W. Which of the following vectors equals the zero vector?

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: In Cartesian space, the direction of the line (x, y, z) = (a, b, c) +r(d, e, f) is represented by…

A: The given line is (x,y,z)=(a,b,c)+r(d,e,f) So, the point (a,b,c) is on the line and (d,e,f) is a…

Q: If i = (a, b, 0), ï = (a, 1, 6), and (1,1, 12) are vectors in R Determine the value of b so that and…

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Q: Given the vectors in 3-dimensional space is a= (a,az.az) and b= (b,b,.b,). The cross product of a…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

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: Prove that if x and y are vectors in R", then |||x|| – ||y||| < ||x- y||. X

A: Given x and y are vectors in Rn we have to prove that x−y≤x−y Since, x=x Hence,  x=x−y+yAdd and…

Q: If a,b,c are vectors such that a.b=a.c,a×a=a×c, then show that b=c

A: Given, a,b,c are vectors such that a·b=a·c, a×a=a×c To prove: b=c

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

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Q: Let u, v, and w be linearly independent vectors. Show that (u+v), (u-v), and (u-2v+w) vectors are…

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Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: Suppose that u, v, and w are vectors such that cu, V) = 3, cv, w> = – 4, cu, wɔ = 7, ||u||= 1 ||v||=…

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Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9,3), v = (-2,6)…

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Q: If a and b are two vectors in 3-space, then axb bxa. Select one: O True False

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Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w .…

A: A vector v is said to be contained in span of set S  (span(S)) if vector v can be written as a…

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: Suppose v1, v2, v3 are vectors in Rn, and that u and w are both in Span{v1, v2, v3}. Prove that for…

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Q: Suppose that ữ, ī, and w are vectors in R3 such that uxu= (2, 7, 3) Find: %3D 1. ūxũ 2. i xữ 3. ūx…

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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: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

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Q: Determine if the following vectors are orthogonal. 4 -4 b = -5 -7

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Q: If î, j, and k are the standard unit basic vectors in 3-space, determine the value of. -G – 3k) + (i…

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Q: 4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east

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Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9, 3), v = (-2,…

A: The given two vectors are u=9, 3 and v=-2, 6 We have to determine whether the given two vectors are…

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Find three different vectors that are in the span of the given vectors. 9- 7 U2 = 4 -2 6. 2

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Q: Which two vectors are orthogonal if given a =,b = and c =

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Let {v1,v2,v3} be a set of vectors in Rn. If "u" is in span {v1,v2,v3}, show that 3u is in span…

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Q: Suppose that u, v, and w are vectors such that Evaluate the given expression. u-v-2w, 4u+vi= (u, v)…

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Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

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Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9,3), v = = (-2,…

A: We can check whether the two vectors are parallel, orthogonal or neither by definition as below.

Q: Suppose that u, v, and w are vectors such that = 6, = -4, = 5, ||u|| = 1, ||v|| = 7, ||w|| = 8.…

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Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (4, 5,-2), v =…

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Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: Let 7 =, if the vector w is in the opposite direction of the vector 7 and w= 3, then u

A: The given vector is u→=3,-4,2, the vector w→ is in the opposite direction direction of the vector…

Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

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Q: If a = (3, 0, -1), find a vector b such that comp, b = 2. %3D

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Q: Let x1, x2, and x3 be vectors in R3. If x1 ⊥ x2 and x2 ⊥ x3, is it necessarily true that x1 ⊥ x3?…

A: Orthogonal vector ( Perpendicular vector): two vectors u and v are orthogonal if u.v=0

Q: Let

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Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

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Q: If u, v, and w are vectors in R° , where u is non zero and u X v = u X w, then v = w. Select one:…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.