Consider a regular hexagon sitting in the xy-plane of R³, centred at the origin. The positive directions of the x-axis and y-axis are labelled as normal below. The positive direction of the z-axis is pointing out of the screen/page. Position vectors u1, pointing to the vertices of the hexagon as shown; each one is a unit vector. U6 are ...) U2 U6 U3 → x U4 U5 Find the vector > u; x uj. i,j=1 i

Q: How many vectors have length 1 and dot product with (-1,7,2)=0?

A: We have to find number of vectors have length 1 and dot product with (-1,7,2)=0.

Q: Solve the problem. Describe all solutions of Ax = b, where 2-5 3 -2 6-5 and b = 4 7 0, -[C].…

A: Given: A=2-53-26-5-470 and b=-38-9. To Do: Describe the general solution in parametric vector form.

Q: 6 2 -6 -5 -4 -3 -2 -1 1 4 6. -2 -4 -5 -6 a. Using geometric vector addition, draw the vector sum a+…

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Q: . Multiplying a vector by a scalar results in: a. a scalar b. a perpendicular vector c. d. In the…

A: 2)Multiplying a vector by a scalar results in  d) a collinear vector. 3) CA→=GE→=b→ GD→= a→ -c→…

Q: O Represent the parabola 4=2文+1 by a vector valued funchion and sketch it (show everything !)

A: A parabola is a conic section. When a plane parallel to another plane and tangential to a right…

Q: Given three points P(2, −2, 1), Q(3, −1, 2), R(3, −1, 1). (a) Find the area of the triangle…

A: given: three points P(2, −2, 1), Q(3, −1, 2), R(3, −1, 1) (a) we have to find the area of the…

Q: Consider the triangle with vertices A(2,3,5), B(-1, 4,4) and C(-2, -1,6). Use vector multiplication…

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Q: 3 -3 2 6 -3 7 (1.8) Consider the set spanned by the columns of B = 6 3 16 9 -3 21| Please write an…

A: Here,B=3-326-3763169-321∴By reducing B into echelon form by applying row operation, we…

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: 2- Two planes are parallel if their normal vectors are orthogonal. False True

A: Two planes are parallel if their normal vectors are orthogonal.

Q: A projectile is shot from the top of a building 96 ft high from a gun at an angle of 30° with the…

A: Giventhat: Height (h) = 96 ft Angle (theta) =30° Muzzle speed =1600 ft/sec Findout the position…

Q: How do you do rotations?

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Q: Find the unit vector in the same directions as v = (-3,1)

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Q: Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+…

A: Given- Let a ∈ ℝn be fixed. Suppose that vectors x, y ∈ ℝn are related by the equation a = x + x·yy.…

Q: 5) 5 li) Given that the vectors a and b are parallel, find the value of x when ()- 4 a and b = 8…

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Q: This doesn't make sense. How does x1-x3=0? shouldn't it be (1,0,0)-(-1,2,-2)=(2,-2,2)? Can you…

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Q: Find a + b, 2a + 3b, |a|, and |a – b|. - а 3 (4, - 3), ь - (-4, 3) a + b = 2а + 3b %3

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Q: For the following three vectors are given in Cartesian coordinates: A₁ = [-4,3], A₂= [13,5], and A3…

A: The given vectors A1=-4, 3, A2=13, 5, and A3=12, 13. We have to find the values of a) A1, A2, A3 b)…

Q: Explain how to solve this question in detailed steps. (13)

A: In subtracting one vector from another vector, its like finding the difference between the two…

Q: Find a + b, 4a + 5b, lal, and la - bl. (Simplify your vectors completely.) a = (-5, 12), b = (10, 4)…

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Q: Simplify the following: u)V-180 (b) For the complex numbers 2 8+15] and zy-3+8, write out and…

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Q: = 2i-3j +3 and -3i +x +2î are orthogonal, then

A: If u and v are Orthogonal then determine x value

Q: Find the angle 0 between the vectors. (G E i+ sin (-)j u=COS V=COS i+ sin

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Q: (b) For the two cases below, circle the case where the length of the cross product between the…

A: The length or the magnitude of the cross product of two vectors: p→, q→ is calculated using the…

Q: TRIANGLES AND VECTORS Dot product of vectors given in component form Find (7, 9)-(-1, -8). 品 ロ后仁可…

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Q: Two forces are acting on a point. The first force has a horizontal component of 5 newtons and a…

A: The complex number z=x+iy can be plotted in the complex plane by moving x units along the real axis…

Q: Find the angle between the vectors a = (4, 4, -2) and b = (5, -3, 3). Solution Since |al = V42 + 42…

A: Given:    a=4,4,-2    b=5,-3,3 The angle between two vectors is given by           cosθ=a·bab

Q: Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer

A: Vectors of Triangle Inequality : u+ v≤u + v

Q: Explain how to solve this question in detailed steps.

A: Definition of Parallel Vectors: Two vectors are considered parallel if they have the same or…

Q: Dot Product Find the dot product of the vectors a = (1, 3, −4) and b = (–2,3,1)

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Q: (b) A vector G is defined as Calculate G = xyl +xzj+yz²k grad(div G) Equation (84)

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Q: 2. Given the vectors and u = (3,−4), v = (−1,2) find |2u + v, |2u|+|v|| Answer: √61,10 + √5

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Q: -3 Are the vectors -3 -4 -8 and linearly independent? -6 3 linearly dependent If they are linearly…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.