Derive the formula for the distance between points P1(p1,q1,z1) and P2(p2,q2,z2) given in spherical coordinates

Q: Sketch the set of points (described in spherical coordinates). ρ = 4

A: Sketch the set of points (described in spherical coordinates). ρ = 4

Q: Explain why in spherical coordinates the graph of = c is a half-plane and not an entire plane.

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Q: Sketch the set of points (described in spherical coordinates). ρ = 2, 0 ≤ φ ≤ π/2

A: GIVEN we need to sketch ( spherical coordinates)  condition ρ = 2, 0 ≤ φ ≤ π/2

Q: Given the point (V3, ,-1) in cylindrical coordinates, what are the spherical coordinates (p, p, 0)…

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Q: If the spherical coordinates (p, 0, ) of a point P are (1, 0,), then the Cartesian (rectangular)…

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Q: Convert the point (x, y, z) = (4, 1, 4) to spherical coordinates. Give answers as positive values,…

A: The spherical coordinates of the point x, y, z is ρ, θ, ϕ where ρ = x2+y2+z2 θ = cos-1zr ϕ = tan-1yx

Q: Let P be a point in R³ with rectangular coordinates (,,-V3). (a) Give the cylindrical coordinates of…

A: We have to convert rectangular coordinates to cylindrical coordinates.

Q: Convert the point (x, y, z) = (5, 3, - 1) to spherical coordinates. Give answers as positive values,…

A: For converting Cartesian to spherical coordinates use the following expression, p=x2+y2+z2 θ=tan-1yx…

Q: Sketch the set of points that are described in spherical coordinates where: TT pS 2, 0<0<2' 2 くp<T

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Q: Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and

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Q: If a point A has the rectangular coordinate (v2, v2, V3), so its cylindrical coordinates are (2, 5,…

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Q: Which statement about spherical coordinates is correct? (a) If φ = 0, then P lies on the z-axis.(b)…

A: To find: The statement that is true. Given: The first statement is φ=0 then P lies on the z-axis.…

Q: Convert the point (x, y, z) = (– 4, 2, 5) to spherical coordinates. Give answers as positive values,…

A: We are asked to convert  to spherical coordinates.

Q: Sketch the set (described in cylindrical coordinates). r = 4

A: GIVEN r=4 we need to sketch the cylindrical coordinates

Q: Convert to spherical coordinates and evaluate: 4-x2-y2 4-x2 -4²+x²+z?)² dzdy dx

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Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Convert the point (x,y,z)=(3,−1,−3) to spherical coordinates. Give answers as positive values,…

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Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

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Q: Let P be the point (4, 1/3, 5) in cylindrical coordinates. Find the x-coordinate of P in Cartesian…

A: Formula: For a point P in three-dimensional space represented with cylindrical coordinates r, θ, z,…

Q: describe the given set in spherical coordinates x2 + y2+ z 2 ≤ 1

A: Given: x2+y2+z2≤1 Spherical coordinates: x,y,z→ρ,θ,ϕ ρ2=x2+y2+z2

Q: Express the equation z = rroot2 cos2tita, which is given in cylindrical coordinates, in…

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Q: 1. Consider a point in Cartesian coordinates given by (-2,2√//3, 4). (b) Find a corresponding…

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Q: Convert the point (x, y, z) = (4, 5, 1) to spherical coordinates. Give answers as positive values,…

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Q: describe the given set in spherical coordinates x2 + y2 + z2 = 1, x ≥ 0, y ≥ 0, z ≥ 0

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Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: 1) Use spherical coordinates to evaluate 4-y² c4-x²-y² 4-x2-y2 Li L y²/x² + y² + z² dzdxdy

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Q: Express the point (x, y, z) = (-2, 2, 2/2) in spherical coordinates.

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Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as

Q: Which of the following is the spherical coordinates of the point (0, v3, 1) which is given by…

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Q: What are the rectangular coordinates of the point whose spherical coordinates are (1,,)? x = 0 y = z…

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Q: a) Convert points P(1, 3, 5), T(0, -4, 3), and S(-3, -4,-10) from Cartesian to cylindrical and…

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Q: Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1, 0, 0) -…

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Q: Find the rectangular, cylindrical and spherical coordinates of point P shown in the figure.

A: Spherical coordinates is Rectangular coordinates is cylindrical coordinates is

Q: Convert the point (x, y, z) = ( – 5, 1, – 1) to 6. spherical coordinates. Give answers as positive…

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Q: Convert the point (x, y, z) = ( – 5, 1, – 1) to | - spherical coordinates. Give answers as positive…

A: To convert the given cartesian coordinates (x,y,z)=(-5,1,-1) into spherical coordinates (rho, theta,…

Q: Convert the point (x, y, z) = (- 5, – 2, 4) to spherical coordinates. Give answers as positive…

A: We have to find the spherical coordinate

Q: Convert the point (x, y, z) = ( – 4, – 2, 2) to spherical coordinates. Give answers as positive…

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Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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Q: Convert the point (x, y, z) = (0, – 3, 2) to spherical coordinates. Give answers as positive values,…

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Q: Convert the point (x, y, z) = (0, - 3, - 2) to spherical coordinates. Give answers as positive…

A: To convert the given point into spherical coordinates (x,y,z)=(0,-3,-2)

Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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Q: 1. Convert the point (1,1, v2) from Cartesian to spherical coordinates. (a) (Vz. vz) (b) (1.#.v2)…

A: Option A is correct answer. Explanation is given below.

Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: Convert the following point from rectangular to spherical coordinates: ( -3/2 -3/6 (p, 0, $) =…

A: The given rectangular coordinates are x,y,z=-322, -362, -32

Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Čonvert the point (x, y, z) = (1, – 5, 3) to - spherical coordinates. Give answers as positive…

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Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

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Q: (a) Convert points P(1, 3, 5), T(0, -4, 3), and S(-3,-4,-10) from Cartesian to cylindrical and…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…