Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly independent? choose If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. (0,0,0) = (-6,-6, -9)+ (3,3, 12) + (-1,–1, 6).

Q: Determine whether or not the given two vectors are parallel.u =〈-3, 1, 4〉, v =〈6, -2, 8〉

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Express the vector P, P2 in the form v = v, i+ v2j + v3k if P, is the point (- 7, - 3,1) and P2 is…

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Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find 1 the area of the parallelogram determined by u…

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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: Let V = {ü, v, w} where й 3 ( — 3, 2, — 3), ў — (3, 5, – 5). - Find ũ that would make a DEPENDENT…

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Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: Let v1 = [1, 1, 0, 2], v2 = [0, 1, 2, 3], v3 = [-1, 0, 2, 1), V4 = [ 3, 1, -4, 0] and b = [4, 3, -2,…

A: Given

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors vi, V2, and v3…

A: Let there exist a, b, c such that0=av1+bv2+cv3

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: Express the vector in the form v = V¡i + v2j + v3k. P2 if P1 is the point (4, -5, 6) and P2 is the…

A: Given :                      P1 4,-5,6 and P2 6,-8,2

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

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

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Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with…

A: Given vectors u=(1, -3, 5)  v=(2, 1,-3)  And line passing of point (1, 2,3)

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: Find the resultant of the vectors A and B. Ả = A = 8a, + 7ay + 2a, B = -Зах — 8ау — ба, Draw the…

A:

Q: Let v,,v,.v be vectors. Show that at least one of the vectors can be written as a linear…

A:

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Determine if the vectors vị = (1,2, 3), v2 = (1,-1,–3), v3 = (1, 1, 1) span R³.

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Q: Find all values of b for which the vectors (2, -4, 5) and (b2, b, 0) are orthogonal. (Enter your…

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Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: Let A, B,C be three points not lying on the same straight line. a. Which set of points P is…

A: Here given A, B, C be three points not lying on the same straight line that means these points not…

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

A:

Q: Determine whether or not the given two vectors are parallel.u =〈4, 2, -6〉, v =〈2, -1, 3〉

A: To determine whether or not the given two vectors are parallel.u=4,2,-6 and v=2,-1,3 By definition,…

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

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Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

A:

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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Q: Are the vectors -5 -3 and 4 linearly independent? Choose If they are linearly dependent, find…

A: Here we have to check the given vectors are linearly independent or not.

Q: Find two vectors j and 02 whose sum is (-3, -4), where j is parallel to (0, 5) while 02 is…

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Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

A:

Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

A:

Q: Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, va, and v,…

A: Please see the below picture for detailed solution.

Q: Suppose u = (-2,–3) and v = (2, –10) are two vectors that form the sides of a parallelogram. Then…

A: The diagonals of the parallelogram are u+v and u-v then we find the lengths of diagonal.

Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

A:

Q: Find three vectors v1, v2, v3 such that (1) any two span a plane, and (2) Span{v1, v2, v3} is also a…

A: Span of two vectors is a plane

Q: Determine every c Є R, for which the vectors [c,1,c], [5,c,4], [9,1,c] are linearly dependent.

A: We will use the property of vectors to determine the values of c for which the given vectors are…

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

A:

Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

A:

Q: Let a and b be vectors on R³. Suppose a = (-2, 3, 482+ 1) and b = ( 8 + 1, -2, 4) What must be the…

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Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.