Question

Given vector \(A = (y^2 - x^2) \mathbf{a}_x + xyz \mathbf{a}_y + (x^2 - z^2) \mathbf{a}_z\) Transform \(A\) into cylindrical coordinate and it's magnitude at point \((1, 30^\circ, 2)\) is equal to .1 \(1.283 \mathbf{a}_\rho - 1.241 \mathbf{a}_\phi + \mathbf{a}_z\) \(0.217 \mathbf{a}_\rho + 0.625 \mathbf{a}_\phi - 3.25 \mathbf{a}_z\) \(0.899 \mathbf{a}_\rho + 0.808 \mathbf{a}_\phi + 12 \mathbf{a}_z\) : Find \(\nabla \cdot (\nabla \times A)\) is equal to .2 00 50 50 : Find \(\nabla \cdot (\nabla \times A)\) is equal to .3 :Find \(\nabla \cdot A\) at point \((2, 2, 2)\) is equal to .4

          Given vector \(A = (y^2 - x^2) \mathbf{a}_x + xyz \mathbf{a}_y + (x^2 - z^2) \mathbf{a}_z\)
Transform \(A\) into cylindrical coordinate and it's magnitude at point \((1, 30^\circ, 2)\) is equal to .1
\(1.283 \mathbf{a}_\rho - 1.241 \mathbf{a}_\phi + \mathbf{a}_z\)
\(0.217 \mathbf{a}_\rho + 0.625 \mathbf{a}_\phi - 3.25 \mathbf{a}_z\)
\(0.899 \mathbf{a}_\rho + 0.808 \mathbf{a}_\phi + 12 \mathbf{a}_z\)
: Find \(\nabla \cdot (\nabla \times A)\) is equal to .2
00
50
50
: Find \(\nabla \cdot (\nabla \times A)\) is equal to .3
:Find \(\nabla \cdot A\) at point \((2, 2, 2)\) is equal to .4

Given vector A = (y^2 - x^2) 𝐚x + xyz 𝐚y + (x^2 - z^2) 𝐚z
Transform A into cylindrical coordinate and it's magnitude at point (1, 30^∘, 2) is equal to .1
1.283 𝐚ρ - 1.241 𝐚ϕ + 𝐚z
0.217 𝐚ρ + 0.625 𝐚ϕ - 3.25 𝐚z
0.899 𝐚ρ + 0.808 𝐚ϕ + 12 𝐚z
: Find ∇· (∇× A) is equal to .2
00
50
50
: Find ∇· (∇× A) is equal to .3
:Find ∇· A at point (2, 2, 2) is equal to .4

Added by Kathy P.

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