Given the vectors a = (1, 2, 3) and b = (1, –1,2), what is the dot product a · b · a? 4 14 (7,1, – 3) (-7, –1,3) (7, –1, –3) (1, –2, 6) (5, –5, 10) does not exist

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: Civen that 1 00 7 -4 -3 3 2 19 -1 1 4 0 1 0 4 3 -1 4 3 0 0 1 4 3 write 4 as a linear combination of…

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Q: AB, BC, AC.

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Q: -14 Given that write 3 -5 -3 -14 ] -5 = 2 -2 -3 1 0 0 −1 −1 as a linear combination of the vectors 1…

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Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

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Q: Find the magnitude of the vectors represented 5 3 1 by (a) (b) |³| (c) 12 4 3 LO 5 1

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Q: For the following three vectors, what is 2. Ć ·(3 Á × B )? В = 3.00î + 3.00ĵ – 4.00k B = - 3.00î +…

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Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

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Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

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Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: Refer to the vectors u₁ to ug. 1 --0--0--0--0--0-0-0-0 U4 = -4 = 1 u6= 4 2 = (c) -4 (d) 1 U2 = 1 2…

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Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: Given the following vectors A = -4a +3a-2a₂ X y B=a_+5a +7a_ X y z C=-2a-4a +6а X y Evaluate |AX…

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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: 1. Find A-C|(B – D) using the following vectors: A= C= D=

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Q: e) Let C be a new base of R3. If the base change matrix, from base A to base C is - 10 55 32 35 -5 3…

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Q: That is not correct. The first Vector answer is [-2/3, -1/3, -2/3] (column wise format.)

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Q: Place the vectors a, b, c, and d in order of length, from smallest to largest. Show your…

A: We have to find length of each vectors first.

Q: Let à = (6, 6) and 6 = (-4, 7). Compute the dot product. ā.b=

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Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Solve the following exercises, you will need to show all your work to receive full credit. Consider…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

Q: Consider B= {(4,6, c-1), (2, 3, 2c), (1, -1, c)} a set of vectors from R³. What are the values of c…

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Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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