a) Give an example of unit vector in R3.

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: 1.) Determine whether the set, together with the indicated operations is a vector space. If it is…

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Q: Write v as the sum of two vector components if v = i +3j and w = 2i+j. O v = (-2i+2j) + (i +j) Ov=…

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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: Given, vector a = (3, 4, -2), vector b = (2, -7, 1), and vector c = (-6, 5, 4). Evaluate |-2b x c|

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Q: Derive the vector triple product formula a × (b × c) = (a · c)b - (a - b)c. . ↳s a hint for a good…

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Q: Find the unit vector of A=3ax+2ay-3az

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

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: Sketch a graph of each vector. 11) b=(-2V2,-1) 12) RS where R= (-6, 1) S= (-8,-10)

A: Solution (11.)

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

A: A vector is written as aî + bĵ.

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: The graph below shows vectors u, v and w. 5- -5 -4 -3 ν 4 3 2 -2 2 3 -1 W -2 -3 -4 -5 Clear All…

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Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Algebra Question

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Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Say that a is a vector (nonzero) in the third dimension. b and c are two other vectors. If a x b = a…

A: Given: The statement is a×b=a×c where a, b, and c are vectors. The vector a is a nonzero vector. To…

Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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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 f: R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation? a. f(x + y) = f(x)…

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Q: Determine the unit vector of r. B. 30 40

A: Explained below

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)