The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j -7k -31 +11]-7k Which statement is right?*

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2),…

A: We have to find a vector of norm 1 which is orthogonal with the vectors u, v and w. Let a, b, c, d…

Q: نقطتان )2( The cross product of the vectors 3ax + 4ay - 5az and -ax + ay - * ,2az is -Зах -11ау -7az…

A: Dot product

Q: Determine whether the set of vectors is orthogonal. 4 2 - 4 -4 - 3

A: To determine Whether these sets of vectors are orthogonal or not.

Q: Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

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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: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

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: The vectors (2, 2, -1) and ( -1, 2, 2) are orthogonal. Divide them by their lengths to find…

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Q: Hello, any help for this problem would be greatly appreciated. Thank you! 7.3

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Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Express the product Ax as a linear combination of the column vectors of A. 2 3][3 -4 + 2 3 5 + 3 |…

A: To find out the correct option.

Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

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Q: s the set of the vectors (:). (2) 1 ) --(;) --() u2 4 U3 = 1 1 1 rthogonal? What is the expression…

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Q: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: 3 And The 'novmal vector to The ve ctou 2i-3)+4k So/ There is 0 number of vectors (in spali)

A: Given a vector, Say, v→=2i^-3j^+4k^ To fin the normal vector of the given vector.

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: The vectors (3, –4,1) and (5,3,3) are orthogonal. True False

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Q: Are the vectors –2 – 8x + 4x², – 4 – 12x – 20z² and -4 – 14x - 6x² linearly independent? choose If…

A: Given three vectors are: −2−8x+4x2, −4−12x−20x2, and −4−14x−6x2 To determine whether the vectors are…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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Q: For the vectors u = (-2,2, -1) and v (-2,1, 3), expressu as the sum u =p n, where p is parallel to v…

A: To find the orthogonal decomposition of the vector u along and perpendicular to v

Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: 8. Consider the vectors [11, 2, 0, 1,0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]; [0, 1, 1, 1, 1,…

A: We will reduce the matrix to see that any row can be made zero or all remain zero after operating.

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: How many of the vectors (n-tuples) (1 2 2 -1 ), (-4 0 0 -4), (-1 1 -2 -2 ), (-2 0 0 -2 ), (-3 -2 -2…

A: If for given vectors the zero vector can only be obtained by their trivial linear combination then…

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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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: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: Suppose that ú, v and w are any three vectors in some R". Show that the set of three vectors: S =…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: The vectors (-3,4, -1) and (3, -4,1) are orthogonal. True False

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Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: 1) Add the (2) vectors; (2, -6) & (-3, 8)

A: The given vectors are (2,-6) & (-3,8). We need to find the addition of the given vectors.

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: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

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Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

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Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0