2(a) Explain centroid of a triangle and rectangle with sketch.

Q: Define parametrization.

A: Parameterization is the process of finding parametric equations…

Q: %3D

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Q: Describe and graph (using a computer) the surfaces a) yz = 4 b) x² - y² = 1 c) 4x² + y² + 4z² − 4y −…

A: a) yz = 4  This represent the hyperbola. And  y = -4 , z = -1  y = -2, z = -2  y = -1, z = -4 y = 2…

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: 18) B. Suppose that rectangle ABCD is dilated to A'B'C'D' using (0, 0) as the center and a magnitude…

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Q: Which three dimensional figures when sliced by a plane cannot have a cross section that is a square?

A: When a rectangular pyramid is sliced by a plane then the obtained section will not be square.

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4 represent in…

A: Given: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4…

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: Let uequals=22iminus−j​, vequals=66iplus+j​, and wequals=iplus+33j.   Find the specified scalar.…

A: Step 1:Given:-u = 22i - j v = 66i + jw = i + 33j  So let's find out 4(u ⋅ v) The notation "u ⋅ v"…

Q: Find the point on the sphere x^2 +y^2 +z^2 =4 which is closer to the point (1,-1,1)

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Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

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Q: Consider the differential equation: dy = y(1+y) dx and the following initial conditions: (i) y(0)…

A: The given differential equation is xdydx=y1+y. The initial conditions are given below:…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: Prove convexity of an ellipsoid in Rn

A: Let us take two points of ellipse joining a line which lies in the domain of ellipse which means…

Q: Scalar mutiple of z=(4,3,-2)

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Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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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: 2) x² + (v + 2)² = 25 Center Radius

A: