Prove that (1, 0, 0, 0) and (√2, 0, 0. √3/c) are unit vectors in the V4 with the metric ds² == (dx¹)² – (dx²)² -- (dx³)² + - 2² (d.x¹)² Show also that the angle between these vectors is not real.

Q: A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar…

A: Two points given in the xy plane  A = (2, -4) and B = (-3,3)   Find: Distance between the A and B…

Q: ▼ ▼ Part A Express your answer as an ordered triplet of components (x, y, z) with commas to separate…

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

Q: Consider the line element of the sphere of radius a: ds2 = a2(dθ2 + sin2 θ dØ2 ). The only…

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Q: 1.3 Give the function f(x,y,z) = 3x? – 2xyz +y² – 10z. Find -at the point (2,1,1). дхду 1.4 Find a…

A: 1.3 Given, fx,y,z=3x2-2xyz+12y2-10z then, differentiating f with respect to y…

Q: Problem 1. Find the Young diagrams corresponding to the matrices 0 0 1 1 0 0 0 1 0 100 0 0 0 0 0 1 1…

A: Given, Two matrices of order 4 x 4 as  0011000101000000 & 0110000000010000

Q: Which of the following statements is true Select one: O " "Sx, y)dxdy gives the area of the graph of…

A: Third option is true f(x, y, z) = f(y, x, z)

Q: Calculate the following commutators: (a) [P, ² ] (b) [â² , p²]

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Q: Suppose thatP = (x, y) has polar coordinates(r, θ ). Find the polarcoordinates for the points:  (−x,…

A: Given: The point P is (x,y). The polar coordinates are (r,θ). The coordinates of the point are…

Q: Consider the integral 2 dy S = + 12ry dx dx where y(x = 0) = 0 and y(x =1) =1. Find the function…

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Q: Vector u = and vector v = . Find (vector u+v) X vector v.

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Q: P.1: Let lu) = (). In) = (). a) Find the norm of Ju) and |v). Are these vectors normalized? b) If a…

A: We have to perform the following operations mentioned above regarding the ket vectors mentioned…

Q: Evaluate the commutator L,, L, L,- (a) h'L, (b) 0 (c) h'L, (d) h°L.

A: In rotational mechanics, Angular momentum holds a similar place as linear momentum. If Net torque on…

Q: Give the square matrix -6 1 A = 0. The eigenvalues of A are:

A: The given matrix is,

Q: Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from…

A: When subtracting vectors, the rule is to graph the first two from the origin and then connect them…

Q: Find the mass of the solid bounded by the planes x+z=1, x-z=-1, y = 0, and the surface y=√z. The…

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Q: Let a=i-2j-2k and b=6i +31 + 2k; Find? (a) a + b and ab (b)-2a+ (c) The magnitude of a and b (d)āx b…

A: Given:-  a→= i^-2j^-2k^b→= 6i^+3j^+2k^ Find:-  a) a→+b→  and a→-b→ b) -2a→+b→3 c) The magnitude of…

Q: the eigenvalues of the following matrix: /2 2 0 220 0 0 A) 0, 1,4 B) 1.2.2 C) 5,0,0 D) 5, 5,0 E) 0,…

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Q: Using the method of separation of variables, find the solution of the following equation Pu, Pu = 0…

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Q: Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following:…

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Q: The Cartesian coordinates of a point in the xy plane are (−3.3, −3.8). Find the polar coordinates of…

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Q: Consider the following. Tis the counterclockwise rotation of 45° in R2, v = (2, 2). (a) Find the…

A: Solution: (a). Let the vector be transformed through an angle of theta, the new direction of the…

Q: Evaluate the integral. dx (х — 4)(x – 3)(x + 5) (Use symbolic notation and fractions where needed.…

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Q: Consider the Initial Value Problem: (a) Find the eigenvalues and eigenvectors for the coefficient…

A: We have given that,  x'1 = -3x1+3x2x'2  = -6x1+3x2 x10 =2x20 =7

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: Let 7 be the vector (5, 6, -7) and the vector (-0.625, 0.469, 0.625). What is ׈ ?

A: Cross product Cross product is a operation on two vectors in three-dimensional space. It results in…

Q: Rectangular coordinates of a point are given by (2, y) and its polar coordinates are given by (r,…

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