Please provide a step-by-step and clear solution to each of the problems below. 1) Parabolic cylindrical coordinates. Parabolic cylindrical coordinates u, v, w are defined in terms of the Cartesian coordinates by 1 X = (u² - v²), y = uv, Z = W. (a) Determine the scale factors of this coordinate system, i.e. hu, h₂, and hw. (b) Using the obtained expressions of hu, h, and hw in (a), form the expressions for gradient (V), divergence (VA), and curl (V x A) in parabolic cylindrical coordinates.

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-4, 0,…

A:

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: (a) Find the parametric equation of the line that contains the two points A = (-4,0, –1) and B (3,…

A: (a) Here first we find vector v = AB = OB-OA, then the equation of line will be (x, y, z) = A + t v…

Q: Eliminate the parameter by finding the rectangular equation. (Show your work.) 1. Choose the simpler…

A: substitute the parameter

Q: 1) The area of the triangle whose vertices are the points P(1,0,2), Q(3,-1,3), and R(4,1,2). 2)…

A: To find the following equations of line , and area of a triangle.  Since you have posted a question…

Q: Complete the parametric equations of the point (-6,-5,-1) and perpendicular to the plane 4x-2y+3z=7…

A: Given query is to find parametric equation.

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answer as…

A: THE GIVEN LINE IS, x=y=z WE CAN REWRITE IT AS, x-01=y-01=z-01 SO, THE DIRECTION RATIOS FOR THE LINE…

Q: An equation allows you to find the x- and y-coordinates of any point on the xy- plane. OA. True B.…

A: Given the statement " An equation allows you to find the x- and y-coordinates of any point on the…

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A:

Q: Complete the parametric equations for the given rectangular equation. 1 -x+3 (a) Rectangular…

A:

Q: 4. Find the intersection of the two planes. T₁: X+ 2y+3z + 1 = 0 T₂: 3x + 2y +z+2 = 0

A: To find the intersection of the following two planes.

Q: Change from rectangular to spherical coordinates. (a) (0, -√3, 1) (p.0.0) =(√10 (6) (4.4, 4√6)…

A:

Q: 1. The three points A = (-2, -4), B= (6,2) and C = (-3,3) are taken as the vertices of a triangle T.…

A: Given that: A=(-2, -4), B=(6, 2), C=(-3, 3)

Q: Use the given equation of a line to find the point, P = line and a vector, v = (Vx, vy), parallel to…

A: given equation of line  x=(1-t)(6, 7)+t(-5, 0) We a have to find a point on this line and a vector…