Calculate the cross product (v + w) × (5u + 4v) assuming that uxv = (1,1,0), uxw= (0, 3, 1), v×w= (2, –1,1)

Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

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

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: Given u, v and w from question 3, find (a) the angle between u and w,

A: u = (4,0,-2) and w = (2,1,6)

Q: Calculate Dot Product Let u = - Compute the following: ū• v ● vū = = (-7,7, 3) and 7 = (3, 4, -2). 2…

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Q: Find the component of the U along V U=(8,2), v=(3,-4)

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Q: Calculate the dot product of u = (-4, -2, 7, -2) and v = (-3, 1,5,8). u. V =

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Q: Let u1 = (4, -2, 1), u2 = (6,3,2) , u3 = (-2,-1,3) find the linear combination v= u1 - 3u2+ 4u3

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Q: If possible express the vector v as a linear combination of V₁, V₂, and V3. =(0, 0, 0), V₁ = (3, -1,…

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Q: Express the following as a linear combination of u=(2, 1, 3), v= (1, -1, 4) and w=(2, 8, 8). (5, 14,…

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Q: Prove the property of cross products: av(btc)=(axb)+ caxc).

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