If the ai+j+k,i+bj+k and i+j+ck are coplanar then the value of 1/1-a+1/1-b+1/1-c=

Dear pallavi

If  the ai+j+k,i+bj+k and i+j+ck are coplanar then  we can write

ai+j+k = x(i+bj+k)  + y( i+j+ck )

so

 a= x+ y ...........1

1= bx +y ...........2

1= x +cy ............3

(2) -(1)           1-a  =-x(1-b)

(3) -(1)           1-a  = -y(1-c)

  so   1-a  =-x(1-b)  =-y(1-c)

 or  1/1-a  +   1/1-b   +   1/1-c  

 = 1/1-a     - x/1-a     -  y/1-a

=1/1-a [1-(x+y)]

= 1/1-a [1-a]

 =1

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