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 in the form

Options

A. `a=1/(abc)[(a.a)(b xx c)+(b.b)(c xx a)+(c.c)(a xx b)]`
B. `1/[abc][(a.a)[b xx c]+(b.a)(c xx a) +(a.a)(a xx b)]`
C. `a=(a.a)(b xx c)+(a.b)(c xx a)+(a.a)(a xx b)`
D. None of these

Answer

D