Question 1. Use the following information about some vectors in R to answer the questions following: x = (2, –1, 3) and y = (-3, 2, 2) XE w =7 y- w = -2 u x v = (4, –2, 4) (a) Find (x x y) × w . (b) Find (x x v) - u. (c) Find (2u – 5v) × (3u + 2v). (d) The area of the parallelogram with vertex at the origin, determined by u + kv and ku + v is 48. What are the possible values of k?

Q: 3. Determine the value of a and b if the vectors à = [a, 26, 32] and b = [49,-91,b] are collinear.

A: Given,            Two vectors are a→=a,26,32 and b→=49,-91,b are collinear.To find : Determine the…

Q: - - 1. If à = 2ảx + 6ảy – 3ả₂ and ☎ = −3ảx – 4ảy – 5ả₂, find a. a unit vector in the direction of A…

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Q: 1. Add the following three vectors to find the resultant vector, R: šj = (-2,0)m, .ž= (0,–5,)m, .řz…

A: 1.   x1¯  =  (-2,0)mx2¯  =  ( 0, -5)mx3¯   =  (3,0)m Now , In the East - west direction ,  we deal…

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: Let i = [-1 4] and j = [-4 1]. Find the following vectors. i = 62 i = -6j = | w = 62 – 6ỹ = = [ -

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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: Let a (6,7, –2) and b = (4, 4, –1) be vectors. Compute the following vectors. A. a + b =( 10 11 -3…

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Q: 5. Write the components of the following vectors: 5a. ˆı, 5b. −7ˆȷ, 5c. 4ˆı + 9ˆȷ, 5d. 5ˆı − 3ˆȷ.6.…

A: The objective of the question is to write the components of the given vectors and to express the…

Q: You are given the following three vectors a = (9 -3 -1) T b = (2 0 2) T c = (-4 0 8) T Find the…

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Q: Determine which of the following vectors are orthogonal to each other: 12 2 X = 3 X2 1 X3 -3 -5 3

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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: a = (3, 2, 4), b = (-3, 3, 0), c = (0, 0, -2) %3D (a) Find a x (b x c). a x (b x c) = || %3D (b)…

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Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: are parallel, orthogonal, or Determine whether vectors V and W neither. If parallel, determine…

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Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: 1. Let x = i +4j + 2k and y = i - 3j - k. In this question, write all vectors in i, j, k notation.…

A: Let (a) To find .(b) To find .(c) To find .(d) To find .

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: a, b, and c are vectors. Then the expression axc+bxa is (a) Meaningless (b) A vector collinear with…

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Q: Determine the vector 2a – b if a = -4i + 5j and b = 7i + 2j. %3D

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Q: the following vectors: u = [− 2,−1,2] v = [1,−1,−4]and w = [4,3,−2], find u x w

A: u=[-2,-1,2]v=[1,-1,-4]w=[4,3,-2]Find u x w.

Q: Find the vectors T, N, and B at the given point. - (²2², ²₁³, t), (1, - ²-₁, -1) = T = N = B = r(t):

A: To find the vectors T, N, and B at the given point, we need to differentiate the position vector…

Q: a. Write the vector (-4,-8,6) as a linear combination of a₁ = (1,−3,−2), ẩ₂ = (-5, -2,5) and a3 =…

A: The given vectors  and .(a) The aim is to write the vector  as a linear combination of the given…