Given the basis B = (000) {E = if the coordinates of ☞ relative to basis B are [] B W = [8] find w

Q: Given vectors u and v in the diagram below, shade in all linear combinations cu + dv for (a) -1 1…

A: (a) Shade the linear combination.

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: Order the following vectors by increasing magnitude. (3,4) (0,-6) (-2,4)

A: Given vector is (3,4) , (0,-6) and (-2, 4). We have to order the vectors by increasing the…

Q: If vector A = [4/1] and vector B = [-3/2] find A-B

A: Here two vectors A and B are given we have to find A-B.

Q: Given that (A x B) x (C x D) = [A,C,D]B - [B,C,D]A, derive (A x B) x (C x D) = [A,B,D]C - [A,B,C]D…

A: To derive the second identity , assuming the truth of the first

Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

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: 9. Given vectors u = [- 2,6.7] and v = [3.1.–4]. determine .

A: From the given problem:   u→=-2,6,7⇒-2i+6j+7kv→=3,1,-4⇒3i+1j-4k   So,   u→×v→=ijk-26731-4

Q: 5) Write the analytical expression of the unit vector for F= 400 i + 700j - 400 k %3D

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Q: If v is any vector and n is any unit vector: (a) Show that v can be expressed as v = (v.) î+ĥx (v ×…

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Q: Let = [-3 1] and = [1 2]. Find the following vectors. [ ]]. ]]. u = 7y= = [1 w = 2x + 7y = [ v=27=…

A: Given: Let x→=[-3  1] and y→=[1  2].

Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: Find the difference vector of the following: and =< ♦

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Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

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Q: {) 0 } A .8 For what values of a is the vector -3a in the span of -2

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Q: 3. 4. If =(-12, 4, 8) the position vector of u is.............

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Q: -{{} O Consider the bases B = Find the B-coordinate vector of i= (2, –1).

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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: Let i = [1 -4] and y = [4 -6]. Find the following vectors. i = 57 ü = 2g =| w = 5i + 2j =||

A: The solution is given below:-

Q: Of the following expressions, select all that are defined. Assume all vectors have 3 components so…

A: Gvien two vectors a and b then

Q: 5. [6.1] If vector ā reaches from the origin to point (5, –7), determine the magnitude of ā.

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Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: Write a in the form of a = a¡T + a„N at t = 0 without finding T and N for r(t) = (2 + t)i+ (t +…

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Q: Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B ×…

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Q: 3.10. Rotate the vectors by 30%. *:[],三闾

A: We have to Rotate the given vectors by 30°.

Q: Find the coordinate vector of v = [-7 [-7 [011], [221] ). −4 -4 -5] relative to the ordered basis B…

A: Vβ​=[−3​0​−2​]   Explanation:

Q: Let = [-5 1] and = [6-6]. Find the following vectors. [ = -6y = [ w = 5x – 6y = [ | v=5z ]]

A: A detailed solution is given below.