Write each vector as a linear combination of the vectors in S. (Use s and s, respectively, for the vectors in the set. If not possible, enter IMP S- ((6, -7, 8, 6), (4, 6,-4, 1)} (a) u-(-54, 127, -128,-72) -(4-10,). (b) (c) W3D

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

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: What is the component form of the vector with an initial point of (-2, 5) and a terminal point of…

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2),(1,-1,-4,0) and (2,1,1,6) vectors in R^4 are…

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Q: Write the vector (-5, -9) as a linear combination of the vectors (-2, 3) and (1, 4).

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix and the…

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 the vector PP, 1. Р.(3,2) P, (5,7) 2. P(-2,-1) 3. Р (3,3) P,(4,-5) P, (5,5) 2

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

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: The two vectors a = (-1,2,-2) and b = (2, -4,-5), are not parallel but are orthogonal. Select one:…

A: Using algebraic operation

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: Find vectors A and B such that A is parallel to (2, 1,-1), B is perpendicular to (2, 1, -1) and A +…

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Q: Express the vector of the form v=vi+ v2j + v3k. AB if A is point (-9, -2, 1) and B is point (-4, -9,…

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Q: In each case, find the linear combination of the first two vectors that is as close as possible to…

A: Both part of the question can be converted into the question based on least squares solution of a…

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: a. Write the vector (-5, 15, 12) as a linear combination of a the form 4a, + 5ã, + 6ã3, which would…

A: Solving system of linear equations we get the result

Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: Determine if the vectors , and are linearly independent.

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A: a) Given:     w=1,1,5, v1=7,7,7      v2=2,5,3, v3=4,1,-1 w=i^+j^+5k^, v1=7i^+7j^+7k^…

Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

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Q: 1. Find the vector 7, in component form, with initial point P(-3, 10, -5) and terminal point Q(1,6,…

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Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Select all vectors perpendicular to the vector (1, 3, -5) O (2, 1, 1) O (0, 5, 3) O (1, 1, 3) O (4,…

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: Express the vector in the form v = vji + v2j + v3k. AB if A is the point (-9, -5, 5) and B is the…

A: A-9,-5,5 and B-4,-12,8

Q: Write the vector (1, 2, –1) as a linear combination (if possible) as of the vectors (-1,2, 1), (2,…

A: Solution: The objective is to determine whether the given vector is linear combination of the given…

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: Identify if the vectors〈-1,2,-1〉and 〈2,-4,-1〉parallel or not

A: Two vectors are parallel if the ratio of each component are equal.

Q: Select all vectors perpendicular to the vector (1, 3, -5). O (2, 1, 1) O (0, 5, 3) O (1,1, 3) O (4,…

A: Given query is to find the perpendicular vectors to the given vector.

Q: Write the vector (7,8, –8) as a linear combination (if possible) as of the vectors (-1,1,2), (2,3,…

A: See answer below

Q: Select all vectors parallel to the vector (1,-3, 5). O (2, -6, 10) 0(-1,3,6) - 15

A: here to we need to find the parallel vectorsto the given vector from the given options. the solution…

Q: 2) Subtract the (2) vectors; (4, 6) & (-8, -10)

A: The given vectors are 4, 6 and -8, -10 We need to subtract the given vectors.

Q: 1. Find the sum of the vectors (3,-1) and (-1,5) and illustrate geometrically.

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

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Q: Find a vector orthogonal to all vectors in the set ((2,1,2), (2, – 2,3)) . Write your answer as an…

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Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

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Q: Express i = (3,7,-4) as a linear combination of i = (1,2,3), ỷ = (2,3,7), z = (3,5,6), also check…

A: see below the answers

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: Find the components of the vector P1P2. (a) P1(3, 5, 7), P2(2, 8, 1) (b) P1(7,−2, -8), P2(0, 0,5)…

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Select all vectors parallel to the vector (1, –3, 5). O (2, –6, 10) O(-1,3,6) - 15 ? 5 )

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Q: Find the vectors u and v whose initial and terminal points are given. Initial Point Terminal Point…

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Q: 24. Write a vector (-3, 22, -3) as a linear combination of the vectors (-1, 2, 3) and (0, 4, -3).

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Q: Express the vector v with initial point P and terminal point Q in component form. P(−8, −7),…

A: Given two points

Q: Are the vectors u=(1,2,-4), v=(-5,3,-7) and w =(-1,4,2) are in the ?same plane

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Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

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Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

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.