Calculate the dot products uv and u w and u. (v+w) and w. v: . -- -- -- U= [- :8] [3] Compute the lengths ||u|| and ||v|| and ||w| of those vectors. Check the Schwarz inequalities |uv|≤|u|| |v|| and v.w|≤||v||||w|. .

Q: Find u · (v x w). (4, 4, 4) (4, 6, 0) w = (0, 0, 9) u = V =

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Q: ||ī|| = Find the length of the vector = 2 -2 Enter `sqrt(a)' for √Va

A: In this question we will find the Length of the vector.

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

A: Solutions

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

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Q: Find the projection of u = onto v = .

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Q: Let / be the line through the point with coordinates (1,-1,0) in the direction of the vector…

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Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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Q: 1: Let u = (-3,2, 4) and v = (2, -4,6). a) Find u o (v), b) Find u x v. c) Find Proj,u.

A: Here given that                        u=(-3, 2, 4)                and  v=(2, -4, 6)

Q: Verif the Caudy - Schwarz inequality and the triangle inequality 4.1 for the vectors. (1926), yie…

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Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

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Q: Let u = h = , V= -3 7 2 and w= For what value of h is w in the plane spanned by u and v?

A: The given vectors  and .The objective is to find the value of  for which  in the plane spanned by…

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→