A plane with equation + += 1 (a, b, c > 0) together with the positive coordinate planes forms a tetrahedron of volume V = abc (as shown in the Figure below) Find the plane that minimizes V if the plane is constrained to pass through a point P = (3,3,5). C=(0, 0, c) A=(a, 0, 0) The plane P B=(0, b, 0) y 9- = 1

Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

A:

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: Find an equation of the plane that is parallel to the line of intersection of the planes x-y+ 2z = 3…

A: To find an equation of the plane that is parallel to the line of intersection of the planes x - y +…

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

A:

Q: Find the area of the surface. The part of the cylinder y² + z² = 9 that lies above the rectangle…

A:

Q: 7. Find the equation of the plane passing through the points (1, 1, 2), (3, –1,6) and (5, 2,0).

A: To find the equation of the plane passing through the given points

Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

A:

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

A:

Q: Find the equations of planes that just touch the sphere (x - 5)² + (y − 4)² + (z − 2)² = 25 and are…

A:

Q: Find the distance between the two parallel planes 2x-y+z=1 and 2x-y+z=3 for both equations, if we…

A: The given equation of two parallel lines are

Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

A:

Q: Find the distance between the given planes: 5x - 3y + z = 2 & 5x- 3y + z = -3 | Upload Choose a File

A:

Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: ane with the equation + + = 1 (a, b, c > 0) together with the positive coordinate planes forms a…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

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

A:

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane : z = 0 means t = 3, so the point of intersection is (-2,10,0). Similarly.

Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

A:

Q: Find the centroid of the triangle if the vertices are  (0,0) , (4,0) and (0,6)

A: Given points are         0,0,4,0,&0,6      And centriod G ?      centriod G= x1+x2+x33…

Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Q2) L, - X+2 +2 ー1 - 2 Frand equaton of plane Coudentg

A:

Q: The point(s) of intersection between the y-axis and the plane 2x-y-z=-6 is/are: O {(x, y, z): x =…

A: The given equation of plane is