(2.3) Prove that each of the following systems a) Parabolic cylindrical coordinates (u, v, z) defined by * = uv, y = (u? – u²], z = z b) Paraboloidal coordinate system (u, v, ) defined by I = uv cos ø, · y = uv sin ø, z = [u? – v²] is orthogonal, and then find the following for each of them: The scale factors, the base unit vectors, the vector de, the element de? and the element of volume dr. [hint: to show that the system is orthogonal prove that h12 h23 = 0] h13 %3D %3D

Q: Express the given parametric equations of a line using bracket notation and also usingi, j, k…

A: To express the given parametric equations of a line by using bracket notation and also using  and…

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A: Direction angle

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A: We have given a spherical coordinates:…

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

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The answers are as follows: 7.The vector equation of the line isr=(7,2)+s(2,−3),s∈R.Option b. is…