If ` vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a` is non-zero vector and `|( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0,` then
a.`| vec a|=| vec b|=| vec c|`
b. `| vec a|+| vec b|+| vec c|=|d|`
c. ` vec a , vec b ,a n d vec c` are coplanar
d. none of these

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.