6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find (u, v). (u, v) = 1 -2 ]

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: Assume that the vectors sint cost X2= sint - cost , and X,= sint +cost sint -cost 0. sint +cost are…

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Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). . u = 5i + j - 9k, v=i4j + 5k (a) (b) u. V u u (c) ||u||²

A: According to Bartleby's guide line we only do first three parts of multi-part questions.Given,

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: Find u. v, uu, ||u||², (u - v)v, and u . u = , V = (a) (b) u. V u . u (c) || u ||2 (e) (d) (u. v)v…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

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Q: Evaluate ( 3+j4)( 3+j4) = A +jB, determine the real component A

A: Given,              (3+j4)(3+j4)=A+jB

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

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Q: line through the variable point A(k+1,2k) meets the lines 7x+y-16=0 ,5x-y-8=0,x-5y+8=0 at…

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: 7. Let u = (2,1, −1) and v = (√√2, 1, 1). Find the decomposition of u into vectors that are parallel…

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Q: If u = -i + 4j - 7k and v = 5i - 2j - 9k calculate the product of u . v  u . v =

A: Use the dot product for finding the product of vector .

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

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Q: Find u v, u u, ||v||², (u · v)v, and u (3v). u = (3, 10), v = (-4, 3) %3D (a) (b) (c) ||v|

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Understand Properties of the Cross Product Given u x = (-4,-3, 4), find (u - 5v) × (ū+3v).

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

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Q: Find the cross and v= product uxv² where û =8i +25 - 2k (-3,-1,8)

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Let u=<-1,1> v=<-3,4> and w=<0,-2> Find u-v+4w

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Q: 2i -1+iy -2 + i) are linearly independent over C ? -1+ 3i)

A: If rank is less than 2 we will get a matrix which is linearly dependent.