If `vecd=vecaxxvecb+vecbxxvecc+veccxxveca` is a on zero vector and `|(vecd.vecc)(vecaxxvecb)+(vecd.veca)(vecbxxvecc)+(vecd.vecb)(veccxxveca)|=0` then (A) `|veca|+|vecb|+|vecc|=|vecd|` (B) `|veca|=|vecb|=|vecc|` (C) `veca,vecb,vecc` are coplanar (D) `veca+vecc=vec(2b)`

Options

A. `|veca|=|vecb|=|vecc|`
B. `|veca|+|vecb|+|vecc|=|vecd|`
C. `veca, vecb and vecc` are coplanar
D. none of these

Answer

c

Explanation

`vecd.vecc=vecd.vecb=vecd .vecc= [veca vecb vecc]`
then `| (vecd.vecc) + (vecd.vecb) (vecc xx veca) =0 `
`or [veca vecb vecc] |veca xx vecb +vecb xx vecc +vecc xx veca)|=0`
`or [veca vecb vecc] = 0 " " ( vecd` is non -zero)
Hence. ` veca,vecb vecc` are coplanar.