1 2 Define an inner product on R² according to Let A -3 (u, v) Au · Av, where · denotes the usual dot product. Compute the distance between u = (1, –5) using this inner product. (3, 4) and v =

Q: Given the inner product space (R³(R),+,.,-), where oy = 3x₁₁ + 2(x₂₁ + X₁3₂) + 3x₂y₂ + 2X3Y3, X =…

A: This is a problem related to inner product space. Please see the next step for details.

Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

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

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Q: Find the cross product a x b. a(t, 2, 1/t), b =(², ², 1) Verify that it is orthogonal to both a and…

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Q: How long will it take to drive 700 km at 100 km per hour, if you take a 1-hour break after every 5…

A: We have to find time taken to drive 700km using given data. We will use formulaes,…

Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

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: Compute the dot product u - V. 6 1) u = 2) u = 5, V = 3 -18] 0, V= -9 25 2 -5 2 1

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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: Find the d. c. of T from definition.

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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: The transformation Po[1, ₂] = cos²0 cos sin cos sin sin²0 [1, ₂] onto the line through the origin…

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Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

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Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: -{{} O Consider the bases B = Find the B-coordinate vector of i= (2, –1).

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Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find a. cos(theta), where theta is the angle between…

A: As we know that; The expression for the dot product between the two vectors u & v is: u·v=uvcosθ…

Q: (2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R.…

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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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: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…

Q: vectors u and v are such that ||u||=9, ||v||=6 and u*v=-1. Using properties of the dot product, find…

A: Given query is to find the value of the Indicated vector.

Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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