If a, b, c are three given non-coplanar vectors and any arbitratry vector r is in space, where `Delta_1=|[r*a, b*a, c*a], [r*b, b*b, c*b], [r*c, b*c, c*c]| : Delta_2=|[a*a, r*a, c*a], [a*b, r*b, c*b], [a*c, r*c, c*c]|`
`Delta_3=|[a*a, b*a, r*a], [a*b, b*b, r*b], [a*c, b*c, r*c]|, Delta_4=|[a*a, b*a, c*a], [a*b, b*b, c*b], [a*c, c*c, c*c]|`
Q. The vector r is expressible as

Options

A. `a=(1)/([a b c])[(a*a)(btimesc)+(b*b)(ctimesa)+c*c(atimesb)]`
B. `a=(1)/([a b c])[(a*a)(btimesc)+(b*a)(ctimesa)+(a*a)(atimesb)]`
C. `a=[(a*a)(btimesc)+(a*b)(ctimesa)+(c*a)(atimesb)]`
D. None of these

Answer

C