Find My for a triangle whose vertices are located at (0,0), (1,0), (1,1) if the density of the triangle is uniform and is equal to p.

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the coordinates of a rectangle with corner points at A: (2,4), B:(2,8), C: (5,8), and D: (5,4),…

A: We have to find co-ordinate after translating 6 units up and 2 units left

Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: Find the distance between two planes if they are parallel x+2y+3z=6 and 2x+4y+6z=5

A: Solution:GIvenx+2y+3z=6  and 2x+4y+6z=5To find the distanceFormula:If θ=0°  then the planes are…

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: 2. Find the volume of the parallelepiped the following 3 vectors describe the edges: i.q=i-2j-3k, b=…

A: The given problem is to find the volume of the parallelepiped from the given following 3 vectors…

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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Q: The square region with vertices (4, 0), (0, 4), (8, 4), (4, 8) is revolved around the line x = -8.…

A: Draw a diagram of the square. Determine the coordinates of the centroid of the square.…

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYk Zk): (1,0,0). (1,0, -1),…

A: Let  S = ∑k=14 Axk+Byk+C-zk2  For minimizing S , we have  ∂S∂A = 0 ,  ∂S∂B = 0  and  ∂S∂C = 0…

Q: Find the volume of the parallelopiped with adjecent edges PQ, PR, PS where P(5,-2,-3), Q(7,1,0),…

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Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: The square region with vertices (4,0), (0, 4), (8, 4), (4, 8) is revolved around the line I = -8.…

A: Consider the given points. First draw the points on the plane. Calculate the coordinates of the…

Q: Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x - 6y + 2z = 5

A: