5. Given three vectors , U V and W u+2v+w=0_and_u•v=3. If ||ū||=||||=2, find . such that

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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Q: -21 6. Find h so that the vectors 1 is in the span of the vectors 4, and -3 -0-

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

A: Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is zero,…

Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

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Q: Suppose u and v are any vectors in R³. Which of the following is not true? Ollu + vll ≤ llull +…

A: To find which of the following properties is not true.

Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: Let u and v be vectors in R". Show that ||u – v||? – 2||u – 2v||2 + ||u – 3v||2 = 2||v||? %3D

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Q: 39. The vertices A, B, C of a triangle have position vectors a, b, c respectively. The area of this…

A:

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

A:

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: The following limit lim Select one: O None of them 8x³y³ (z,y) →(1,2) 2x - y O equals 12. O equals…

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Q: 7. Let -3 6 -0--0-0-H [-] 8, V3 11 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are…

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Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

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Q: Let -3 ----------- V3 2 V1 = 6 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are in…

A: Let and

Q: If some p vectors can span V, then dim V= p True False

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Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: 2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b…

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Q: The vectors (2,10, 4) and (1, 3, x) are orthogonal if and only if x= -8. Ignore "Give your reasons"…

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Q: (In set notation: (| x ER).) In the following, determine whether the statements are True or False,…

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Q: 5. Suppose that a, b and care vectors such that |a| = 2, |6| = 1, || = 5, a·b = 0, a. c = 3 and b c…

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Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: 2. Let a, b, c, and d be algebraic vectors in R3, For parts (a) and (b) below, state which theorems…

A: The dot product of the two vectors A→ and B→ is given by the following: A→·B→=||A→||·||B→||·cos θ…

Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

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Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

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Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

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Q: Let u, v and w be three vectors in R³. Which of the following is not defined for all u, v and w?…

A: Here u , v and w are three vectors in R3.  We find which of the given is not defined for all u , v…

Q: 7 Let a and b be vectors in R" such that ||a||=||b||=2 and (a,b) = 1. Then ||ab||= ...

A: Let a and b be vectors in ℝn such that  a=b=2 and <a,b>=72 . Then we have to find the value of…

Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

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Q: Show all the work asap

A: Step 1: Step 2: Step 3: Step 4: