Solve the following geometric problems by Lagranges
Chapter , Problem 26(choose chapter or problem)
Solve the following geometric problems by Lagranges method. (a) Find the shortest distance from the point (a1, a2, a3) in R3 to the plane whose equation is given by b1x1 + b2x2 + b3x3 + b0 = 0, where (b1, b2, b3) = (0, 0, 0). (b) Find the point on the line of intersection of the two planes a1x1 + a2x2 + a3x3 = 0 and b1x1 + b2x2 + b3x3 + b0 = 0 that is nearest to the origin. (c) Show that the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid x2 a2 + y2 b2 + z2 c2 = 1 is 8abc/3 3.
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