2. Given the vector a = (3,-4,5) and vector b = (-2,3,1) determine the following in the most simplified and exact form a) The magnitude of läl b) The coordinates of 2a - 3(a + b) c) axb c) Draw the vector a=(3,-4,5) (use a ruler)

Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point…

A: The Parametric equations of the line are the components of the vector equation , and have the form…

Q: Q7) If -) -) -() a) Using these vectors, Draw diagrams to represent: 1) a +b 2) с - Ь 3) 3c -a b)…

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Q: 3. Determine if the sets of vectors given are LI or LD and explain how you know. a) {(3,4),…

A: Here we apply theorems from linearalgebra.

Q: Find the angle between u = (2,3,1), and v = (-3,2,0)

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Q: A triangle is formed by A = (3,3,1), B = (0, 1, 5), and C = (1, -4,-1). a. What are the angles of…

A: A triangle is formed by A=(3,3,1), B=(0,1,5) and C=(1,-4,-1).We need to find:a the angles of this…

Q: Are the vectors (1, 2, 3, 4), (2, 3, 4, 5) and (3, 4, 5, 6) lin indep?

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Q: 4) Consider the vectors u = [3, -2] and v= [-5, 4], write a = [-24,18] as a linear combination of u…

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Q: 7) Relative to an origin O, the position vectors of the points A and B are given by OA P (-) and OB=…

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Q: 8) Given the vectors (5, 5) & (5, -5); both vectors start at the origin, find "e", the angle between…

A: Vector is a quantity that has direction as well as magnitude. In coordinate system, length of vector…

Q: 10. What is the cosine of the angle between the vectors U = (0, 1,0) and V = (2, 2, 1) ? a) 10, b)…

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Q: What is the angle in radians between the vectors а %3 (6, 8, -2) аnd b = (-7, 7, 0)? Angle:…

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Q: i) ii) Draw a vector diagram for the cyclist's trip. Find the distance covered by the cyclist. (Give…

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Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: Assume b = i +3+k What is the angle that vector 6 makes with z axis (with k unit vector)? Report the…

A: Given vector b→=i^+j^+k^ let a→=k^ We have to find the angle between b→=i^+j^+k^ and a→=k^

Q: a) à = [ 7₁ -2], 6 = [2, -5] b) c = [ 3,5], j = [1, 2]

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Q: Vector A has a magnitude of 2.5 m/s at a direction of 18 degrees and Vector B has a magnitude of 4.5…

A: A) It is given that vector A  has a magnitude of 2.5 ms at a direction of 18° and vector B has a…

Q: Q.1) Choose the correct answer for the following: (choose 5 only) 1- The vector from point P=(2,2,1)…

A: This question can be solved using the concept of vectors.

Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

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Q: A vector v is defined with initial point P = (2, -6) and terminal point Q = (-3, -2) a)  Graph the…

A: Given  A vector v is defined with initial point P = (2, -6)  terminal point Q = (-3, -2)

Q: What is the angle in radians between the vectors a = (6, 8, -2) and b = (-7, 7, 0)? Angle: (radians)

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Q: 3) Let a = 3i, b = i + j. Find 5a + b. A) 11i + j B) i+ 16j 4) Let a =(3, 8), b = (-5,9). Find a +…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 8. Given vector v = (4,-5) a) If we want to represent v in the form v= AB where A = (-2, -3), what…

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Q: Triangle CDE with vertices C(-1. 3). D(4,2). and E(3, 1): a) translated along the vector (-3. -7) b)…

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Q: nd he position vector in the form of xr+ yr for the vector that starts at the point (-1, 2), ends at…

A: Given query is to find the vector ,it's magnitude and direction.

Q: 5) Prove: u-v=v-u for vectors u, v in V. Show all steps clearly, do not skip steps! Use vector…

A: Here, we just need to use the commutativity of the underlying field, here I have assumed the field…

Q: Prove: u-v=v-ü for vectors i,v in V₁. Show all steps clearly, do not skip steps! Use vector…

A: we will take vector u and v then use out comes of dot product to prove it commutative  Values of dot…

Q: Relative to a fixed origin, the points A, B and C have the following position vectors 2 1 0-0) 3 and…

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