Let u = (-3, 2) and v = (6, –2). a) Find u – 3v. b) Find Ju + v|. c) Find u· v. d) Are u and v orthogonal? Explain.

Q: 23. Evaluate (x8(x² - 2x - 3)dx A)1 BIO C)-I D12 E)-2 24. For a constant vector E, find the constant…

A: Let us solve above problem.

Q: a = 3i - j - 4k, b = 2i +4j - 2k, c = -i +6k a. 4a - b b. b * (c - a) c. ||a * b|| d. the angle…

A: Solution : Given, a=3i-j-4k b=2i+4j-2k c=-i+6k a.) 4a-b=4(3i-j-4k)+2i+4j-2k =14i-18k b.)…

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Calculate v × w. v = 〈2, 0, 0〉, w = 〈-1, 0, 1〉

A: Given vectors are v=2, 0, 0 and w=-1, 0, 1. To calculate: v×w Solution: Given vectors can be written…

Q: Find u v. u = i - 9j v = -4i + j u v =

A: We can solve this as follows:

Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

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Q: Determine whether u 17. (Notation means perpendicular; i.e., u v means u and u are orthogonal.) (a)…

A: If the vector two vectors are orthogonal then their dot product is zero.The given vectors are:Now…

Q: Find the cross product a x b. a(t, 2, 1/t), b =(², ², 1) Verify that it is orthogonal to both a and…

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Q: Q2: Use vector to check whether the points A (4,3,2), B (4,3,0), C (4,0,0), and D (4,0,2) are…

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Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

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Q: Evaluate f z²dz where C is the contour |z| = 2-

A: We can directly use cauchy Goursat theorem to give the value of the given integral about given…

Q: Find u x v, v x u, and v x v. u=i-j-k, u x V (a) (b) (c) V x u VX V v = 5i + 5j + 5k

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Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

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Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: 9. Let b, and b, be any real numbers with | b, |31 and | by151. Let u- VI - bịi + b, Vĩ – bị j +…

A: Consider the given vector: Here the objective is to prove that the given vector is a unit vector.

Q: gj Let v= 2; tj V = 2; +j and w=i+2j. Sketch 20, and

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Q: 2. o PQRSTU is a regular hexagon. Let PO = u and RS = v. Express vector TS in terms of u and v.…

A: Given that,In vectors, two vectors are said to be equal if their magnitude are equal and their…

Q: [10 670 -1 3 0, B = 3 1 -2,C= L2 2 1 Let A = 1 -2 31 2 -5 51 -31 - 9 17 a) Find A-¹, then use it to…

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Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

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Q: let v =〈−2, 5〉and w =〈3, −2〉. Sketch v, w, and 2v − 3w.

A: Given vector:                   v=-2,5 and  w=3,-2   Algebra of vectors: Let v = x1, y1 and w =  x2,…

Q: Make all obvious simplifications.

A: We have to solve

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar u - v.

A: Given u=2i-5j, v=-3i+7j.

Q: Let a . Find a unit vector in the direction of a = 1 35 i + 5 √35 =j+ k 3 35 X Invalid notation.

A: Let's find unit vector in the direction of a.

Q: Ifv+w= and v = [1]. C W= , compute and draw the vectors v and w.

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Q: Consider each A and B vector, make each of the following below TRUE or FALSE, and give brief…

A: To prove: A+B→ &lt; A→OrA+B→2 &lt; A→2…

Q: Q2: If it wasA = 3i -j+2k , B = 2i + 3j -k find 1. 4Ã + 2B 2. ÀxB 3. The angle between the two…

A: we know thatA→=ai+bj+ck=a2+b2+c2sinθ=A→×B→A→B→A→×B→=ijkabcnlmwhere…

Q: Vectors. v=i-2j+k, w= i +2j-3K a) Compute the length of V-W.

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Q: Find the angle <ABC given the points A = (0,2,2) B=(-1,0,1) and C= (0,-1,2) Hint:- Find the…

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