If (2,-1,3) is the root of the perpendicular drawn from the origin to the plane, then the equation of the plane is
(1) 2x+y-3z+6=0
(2) 2x-y+3z-14=0
(3) 2x-y+3z-13=0
(4) None of these

Dear Student,

Let the equation of any plane passing through P(2,-1,3) isa(x-2)+b(y+1)+c(z-3) = 0Where a,b,c are the direction ratios.Since point O(0,0,0) is perpendicular to the foot of the plane at a point P(2,-1,3)Direction ratios of OP = 2,-1,3Since the line OP is perpendicular to the plane, therefore the direction ratios of the normal to the plane is proportional to the direction  ratios of OPRequired equation of plane is2(x-2)-1(y+1)+3(z-3)=2x-y+3x-14 Ans 

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