Let ū = -27+ 95 and v = 4i- 7j. Compute each of the following. %3D (a) 2u – 30 (b) ||ū+ T|| Find a unit vector in the direction of o = (-1,2, 3). Find the value(s) of a for which ở = (-1, 2a – 1,3) and w = (2,2a + 3, 11-1

Q: Express the vector = [4] à = vi+ as a a linear combination of ₁ = [] [1] and = [] 02 V2-

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Q: Calculate [1, 2, 2] x [5, -5, -1] -

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Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

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: Suppose u = (-6,4, –5). Mark each vector below with a "T" if it is perpendicular to u, and an "F" if…

A: The given vectors u=-6, 4,-51. 2, 3, 02. 5,-2, 23. 9,-24,-304. -5,-4,-1

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: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

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Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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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: What value of a will make the vectors (-2, x, 1) and (2, –1, 1) orthogonal? Select one: O a. 3 O b.…

A: For orthogonal, dot product of two vectors are zero.

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: p (x )EP 2 (R ), p (x ) = 3x? +x - 5 of the vector {1,x 1,x +1} Based on base Which of the following…

A: Given:  p(x) = 3x2+x-5

Q: Find Vectors and Perform Vector Operations in R³ Let a = (0, – 5, 5) and 6 = (4, 2, — 5). Find – 2ā…

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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: 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: In a standard Cartesian coordinate system a vector, R, has an x-component of + 5.0 m and a y-…

A: In a standard coordinate system a vector R has an x- component of +5.0 m and a y- component of -4.0…

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: 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: 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: 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: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: Solve the following exercises, you will need to show all your work to receive full credit. Consider…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. Find Ar for A = and z= Az =

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

A: A detailed solution is given below.

Q: Let u = [1, -6, 3] and v= [-3, 3, 0]T. Find the vector w = 3u - 2v and its additive inverse. W= W=…

A: The given vectors and .We have to find the vectors and find its inverse.