Q1) Find the point closest to the origin on the line of intersection of the planes y+2z=12 and x+y=6??

Q2) 1. Find (i) a point within a triangle such that the sum of the squares of its distances from the three vertices is minimum, (ii) the dimensions of the closed right circular cylindrical can of smallest surface area whose volume is 16 pi cm3

Q3) 1. Use Langrage method of undetermined multipliers to evaluate: (i) the volume of the greatest rectangular parallelepiped that can be inscribed in the ellipsoid 36 x2 +9y2 +4z2=36 and (ii) the extreme values of x2 y3 z4subject to the condition

x+y+z=1

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