Find the area of the parallelogram with vertices K(1,2,3),L(1,3,6),M(3,8,6), and N(3,7,3)

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: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Let x, y, u and v be row vectors in R' obeying: х%3 (2, -1,3), у%3D(-3, 2, 2), and suppose that X •w…

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Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: If the vectors (y, x, i+ 2) and (x, 1 + y, –1) in C³ are orthogonal and if y + 9 -1, then the…

A: 1st we will find x and then its conjugate

Q: 15. Given three independent vectors w, "'z innd wz, let 2 2=[Wi #2 #3 2 1 0 1 c Then, the vectors v,…

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Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: Find the magnitude R and direction 0 of the resultant vectors. 7.0N 5.0N 5.0N 6.0N 2.5N 80 20 30 10…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: Which of the following pairs of vectors are linearly independent? u = (1,0) and w = (0,2). u = (1,2)…

A: Given: Some pairs of vectors. To find: Which of the pairs are linearly independent. Linearly…

Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

A: According to our guideline we are supposed answer only the first question if you want any particular…

Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

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Q: Which of the following pairs of vectors are linearly independent? Du = (1,2) and w = (2,1). Ou=…

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

Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: Given vector U= ⟨1,-1⟩ and V=⟨1,1⟩, find a linear combination of the vectors u and v of the form aU…

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Q: For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?

A: t+3  &  2t+c2+2 Now since these vectors must be linearly independent, therefore…

Q: Let x, y, u and v be row vectors in R' obeying: x = (2, -1, 3), y = (-3, 2, 2), and suppose that X…

A: Note : “Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: Find the value of k for which the vectors 4 and 4 k are orthogonal. k =

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Q: For what value or values of k the vectors V1 = (1,0, –2,0), V2 = (-1,k,–2,0), V3 = (1,1,1,2) are ▼4…

A: A set of vectors are linearly dependent if there exist scalars not all zero such that  . A system…

Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: Which of the following sets of vectors in R² is linearly dependent? A. {(1,0), (0, 1)} B. {(1,0),…

A: A set of vectors is said to be linearly independent if the matrix with these vectors as columns has…

Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: 5. Find a nonzero vector orthogonal to the plane through the points P.Q,and Rand the area of the…

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Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

A: Given u=(1,2,-1) and v=(3,-1,2) be the two vectors in R3 . From the options we have to find which is…

Q: Which of the following sets of vectors in Rª are linearly dependent? (a) (3,8, 7, – 3). (1, 5, 3, –…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: Which of the following vectors in R4 has the largest mangnitude? A. (4,0,0,-1) B. (0, -3,3,0) C.…

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Q: . Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find…

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: Consider the vectors u = (1,2,3) and v= (2,3, 1) in R. (a) Write w = (1,3, 8) as a lincar…

A: Since we answer only 3 sub-parts, we will answer the first 3. Please resubmit the question and…

Q: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

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Q: Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]? O a) [4, 2, -2] b) [5, 7, 6]…

A: Given vectors  [1,1,1] and [1,2,3] For coplanar with another vector, the determinant should be zero.…

Q: This Linear Algebra and Multivariate Calculus Course ,      Consider the vectors u = [3,-1,2], v…

A: given the vectors u = [3,-1,2], v = [-2,0,2] and w = [1,-1,-2 ]. we need to find the angle between…

Q: Which of the following collections of vectors are linearly independent in R3? (a) (1, 1, 1)T , (1,…

A: Vectors are said to be linearly independent when the determinant is not zero. a. Since the…

Q: 11. What is the vector which is orthogonal both to 9i + 9j and 9i + 9k? B. 81i – 81j – 81k A. 81i +…

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Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: Consider the vectors u =(1,0,4) and v =(-4,11,-4) in R3. If it is known that -3u" +w =v° then w…

A: From the given problem: u=1,0,4; v=-4,11,-4 So, -3u=-31,0,4=-3·1,-3·0,-3·4=-3,0,-12

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: 2. Determine the value of c, so the given vectors are perpendicular: u=[-4c, 3], v = [-1, 2]

A: L

Q: Let x, y, u and v be row vectors in R obeying: x = (2, –1, 3), y = (-3, 2, 2), and suppose that X .…

A: Given is: x=(2,-1,3)  y=(-3,2,2)x·ω=7,  y·ω=-2u×v=(4,-2,4) Note: According to the company…

Q: For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and…

A: The vectors are linearly independent if the matrix formed from these vectors has non zero…

Q: Which of the following vectors is parallel to the vector v -2i +j-2k O 4i-2j+ 4k O 2i-j-2k O 2i…

A: the vector will be parallel if they are multiples of one another that is u=cv

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: Given u, = (1,1,2),u, = (1,–1,22),u, =(1,–2,0) three vectors in R a. Find all the values of A for…

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Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: Which of the following vectors is parallel to the vector v = 2i -j– 2k O 4i – 2j + 4k O 2i + j+ 2k…

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Q: 22. Consider the following set of orthogonal vectors, Vi = (1, – 1, 2, – 1), v2 = (-2,2, 3, 2), v3 =…

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Q: ) Find the cross product of the given vectors e = (6,-2,3) and f= (2,5,-1).

A: Given that  e= (6,-2,3) and f= (2,5,-1). We find vector cross product of this given vector.…

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors 3 3 V1 = 0 and vz =…

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