Question

Let a,b, and c be three real numbers satistying `[a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0]` Let `omega` be a solution of `x^3-1=0` with `Im(omega)gt0. I fa=2` with b nd c satisfying (E) then the vlaue of `3/omega^a+1/omega^b+3/omega^c` is equa to (A) -2 (B) 2 (C) 3 (D) -3

Answer 1

Correct Answer - D
We have
`[(a,b,c)][(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
`implies a+8b+7c=0,9a+2b+3c=0,7a+7b+7c=0`
`impliesa=1,b=6,c=-7`
Clearly `P(a,b,c)` lies on the plane `2x+y+z=1`
`:.7a+b+c=7+6-7=6`