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(a) In Cartesian coordinates, the unit vectors r and φ are related to the unit vectors...
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the...
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the cross products #x f, #x θ, PX φ, θ 0, θ >< φ, and φ >< φ. (b) Express x, y and z in terms of, О and ф. (c) Check the divergence theorern for the function u = r , using for volume the sphere of radius 13] R, centered at the origin, i.e. show that dä -JyV-üö)dr.
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addi...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z)...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es ...
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort...
TO SOLVE Exercise 27.4 (truncation) For fC(R), show that there exists φ E (R) that agrees with f ...
This is a Fourier Analysis Question
TO SOLVE Exercise 27.4 (truncation) For fC(R), show that there exists φ E (R) that agrees with f on [-1, 1]. FOR REFERENCE, DO NOT SOLVE The basic idea for generalizing the notion of function in the context of distributions is to regard a function as an operator Ty (called a functional) acting by integration on functions themselves: and integration by parts shows that Ty(y) - 15.1.7 Definition (R) (or (I) will denote the...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a un...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a unit timelike vector, it is always possible to find a Lorentz transformation such thawill have components (0,0,0,1). Show that if k" is a null vector, i is always possible to find a Lorentz transformation such that k" has components (1,0,0,1). Hence show that if UV,-0, and U"is timelike,...
Solve all parts thanks <Extra Credit 2 Force Vector Directed along a Line Three-dimensional Cartesian force...
Solve all parts
thanks
<Extra Credit 2 Force Vector Directed along a Line Three-dimensional Cartesian force vectors are used throughout engineering mechanics. The generic force vector is represented as follows: F= F,i+Fyj + F kwhere F is the force vector and Fr, Fy, and F, are the vector's i, j, and k components, respectively. The force vector has a magnitude F F2 +F3 + F2. The vector's I 1 Figure < 1 of 2 > C 13/12 5 F =...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
Express Fas a vector in terms of the unit vectors i, j and k (present your...
Express Fas a vector in terms of the unit vectors i, j and k (present your answer with 3 significant figures). Please enter your answers in the form of Ai +Bj +Ck. z - F = 60 N 1101 40 50 Dimensions in millimeters Determine the angle in degrees between F and the y- axis. z - F = 60 N 1101 40 50 Dimensions in millimeters 300 mm 150 mm 200 mm Use the vector product treatment to express...
BOX 5.1 The Polar Coordinate Basis Consider ordinary polar coordinates r and 0 (see figure 5.3)....
BOX 5.1 The Polar Coordinate Basis Consider ordinary polar coordinates r and 0 (see figure 5.3). Note that the distance between two points with the same r coordinate but separated by an infinitesimal step do in 0 is r do (by the definition of angle). So there are (at least) two ways to define a basis vector for the direction (which we define to be tangent to the r = constant curve): (1) we could define a basis vector es...
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the cross products #x f, #x θ, PX φ, θ 0, θ >< φ, and φ >< φ. (b) Express x, y and z in terms of, О and ф. (c) Check the divergence theorern for the function u = r , using for volume the sphere of radius 13] R, centered at the origin, i.e. show that dä -JyV-üö)dr.
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort...
This is a Fourier Analysis Question
TO SOLVE Exercise 27.4 (truncation) For fC(R), show that there exists φ E (R) that agrees with f on [-1, 1]. FOR REFERENCE, DO NOT SOLVE The basic idea for generalizing the notion of function in the context of distributions is to regard a function as an operator Ty (called a functional) acting by integration on functions themselves: and integration by parts shows that Ty(y) - 15.1.7 Definition (R) (or (I) will denote the...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a unit timelike vector, it is always possible to find a Lorentz transformation such thawill have components (0,0,0,1). Show that if k" is a null vector, i is always possible to find a Lorentz transformation such that k" has components (1,0,0,1). Hence show that if UV,-0, and U"is timelike,...
Solve all parts
thanks
<Extra Credit 2 Force Vector Directed along a Line Three-dimensional Cartesian force vectors are used throughout engineering mechanics. The generic force vector is represented as follows: F= F,i+Fyj + F kwhere F is the force vector and Fr, Fy, and F, are the vector's i, j, and k components, respectively. The force vector has a magnitude F F2 +F3 + F2. The vector's I 1 Figure < 1 of 2 > C 13/12 5 F =...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
Express Fas a vector in terms of the unit vectors i, j and k (present your answer with 3 significant figures). Please enter your answers in the form of Ai +Bj +Ck. z - F = 60 N 1101 40 50 Dimensions in millimeters Determine the angle in degrees between F and the y- axis. z - F = 60 N 1101 40 50 Dimensions in millimeters 300 mm 150 mm 200 mm Use the vector product treatment to express...
BOX 5.1 The Polar Coordinate Basis Consider ordinary polar coordinates r and 0 (see figure 5.3). Note that the distance between two points with the same r coordinate but separated by an infinitesimal step do in 0 is r do (by the definition of angle). So there are (at least) two ways to define a basis vector for the direction (which we define to be tangent to the r = constant curve): (1) we could define a basis vector es...
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