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

Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: f) Every continuous map T² RP2 is homotopic to the constant map.

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Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

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: 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: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: Find the surface area of helioid equation (spiral ramp vith vector r Cu,v) = LucosV, usinv, v). %3D

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Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

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: Q) write down the application of cross dot scaler triple and vector triple product ?

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: What are the coordinates of the top point of an equilateral triangle if the corners of its base are…

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Q: 3. This problem is about set addition and subspaces. Let d and d2 , and V = span{di}, U = span{d2}.…

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Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain