If `veca, vecb, vecc` are three given non-coplanar vectors and any arbitrary vector `vecr` in space, where `Delta_(1)=|{:(vecr.veca,vecb.veca,vecc.veca),(vecr.vecb,vecb.vecb,vecc.vecb),(vecr.vecc,vecb.vecc,vecc.vecc):}|,Delta_(2)=|{:(veca.veca,vecr.veca,vecc.veca),(veca.vecb,vecr.vecb,vecc.vecb),(veca.vecc,vecr.vecc ,vecc.vecc):}|`
`Delta_(3)=|{:(veca.veca,vecb.veca,vecr.veca),(veca.vecb,vecb.vecb,vecr.vecb),(veca.vecc,vecb.vecc,vecr.vecc):}|, Delta=|{:(veca.veca,vecb.veca,vecc.veca),(veca.vecb,vecb.vecb,vecc.vecb),(veca.vecc,vecb.vecc,vecc.vecc):}|,`` "then prove that " vecr=(Delta_(1))/Deltaveca+(Delta_(2))/Deltavecb+(Delta_(3))/Deltavecc`

Options

A. `r=(r b c)/(2[abc]) a + [rcb]/(2[abc]) b+ [cab]/(2[abc])`c
B. `r=(2[abc])/[abc]a + (2[rcb])/(abc) b + (2[rab])/[abc]c`
C. `r=1/[abc][(abc)a+(rca)b +(rab)c]`
D. None of these

Answer

C