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 T uesday, November 22, 2022

Home  MATHEMATICS  Find the Jacobian

Find the Jacobian · I) Parabolic cylindrical coordinates · where · Where · Where · Solution:

I) Parabolic cylindrical coordinates where

Find the Jacobian

x, y, z u1, u2, u3 x = (u2 − v2), y = uv, z = z −∞ < u < ∞, v ≥0, −∞ < z < ∞

u ≥0, 0 ≤ v < 2π, ; , −∞ < z < ∞

α ≥0, 0 ≤ β ≤ π 0 ≤ γ < 2π

x = (u2 − v2), y = uv, z = z −∞ < u < ∞, v ≥0, −∞ < z < ∞ Send Email *

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 T hursday, November 24, 2022

Home  MATHEMATICS  The eight vertices of a rectangular prism are as follows, Find the coordinates of the vertices after the prism is rotated counterclockwise about the zaxis.

Question

The eight vertices of a rectangular prism are as follows:

Find the coordinates of the vertices after the prism is rotated counterclockwise about the zaxis through

Solution

Here and The prism is rotated counterclockwise about the z -axis then now we first find

then

Now here

The eight vertices of a rectangular prism are as follows, Find

the coordinates of the vertices after the prism is rotated

counterclockwise about the z- axis.

V1 = (0, 0, 0), V2 = (1, 0, 0), V3 = (1, 2, 0), V4 = (0, 2, 0) V5 = (0, 0, 3), V6 = (1, 0, 3), V7 = (1, 2, 3), V8 = (0, 2, 3)

θ = 60∘

θ = 60

V − = (x− 1 , y − 1 , z − 1 ) Here V1 = (0, 0, 0)

V − = (0, 0, 0) V − = = (x− 2 , y − 2 , z − 2 ) V2 = (1, 0, 0) x2 = 1, y2 = 0, and z2 = 0 Send Email *

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