all pairs Let V be the (X; Y) of real t he set of numbers Fuge ther with following operations ? (R, Y% ) Đ (Xs, Ye ) =(X, + Xq + 4, Y, + Yx) て a show that Vector. addition is a ddition is assoc iative, (X,,Y;) ® (X=, Ya) o (Xs, Y;] 6) and show space. b, that V is hot Vect or

Q: Verify that this is a vector set check each property(assoctive, etc): Y = (yo, y#) (xo + yo + 1, x#…

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Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: 37 Express the following as a single fraction. 2 1 x-1 x A. X-1 (x-1)x x+1 B. (x-1)x D. (x-1)x E. It…

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

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

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Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

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Q: Consider the array of vectors in the figure below. +y G H. R K A L 1. A + B + C + D + Q + H + Í + J…

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: (c) Determine whether the set R², with the operations (x₁, y₁) + (x₂, y/₂) = (x,,0) and c(x, y) =…

A: Let V be the vector space if  1 If u,v∈V  then u+v ∈V 2.  u+v=v+u 3. (u+v)+w=u+(v+w) 4. Identity…

Q: Let u = (5,-5, -7) and 7 = (-6, 1, 2). Compute the following: úxv= v X ū= úxu 3 (u xv) = ū × (30) =…

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Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 3) Verify that it is orthogonal to both a…

A: Given vectors are  a={4,5,0} and b={1,0,3} We have to find a×b

Q: Let à = (6, 6) and 6 = (-4, 7). Compute the dot product. ā.b=

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Q: Find w such that 2u + v – 3w = 0. u = (2, 7, 5, 0), v = (-3, 1, W =

A: Addition and subtraction of two vectors: Add or subtract the necessary components to add or subtract…

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: -1 X1 Let v = Find a vector x = x2 such that 3v +x = |2|

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Q: Calculate the dot product of ?=(−4,−2,7,−3)and ?=(−3,1,5,8)

A: Given vector is u→=−4,−2,7,−3 and v→=−3,1,5,8. We have to calculate the u→⋅v→.…