Question

If `vecx.veca=0vecx.vecb=0 and vecx.vecc=0` for some non zero vector `vecx` then show that `[veca vecb vecc]=0`

Answer 1

Since, `vecx` is a non-zero vectors, the given conditions will be satisfied if eitherm (i) vectors, `veca , vecb and vecc` are zero or (ii) `vecx` is perpendicular to vectors, `veca, vecb and vecc`.
in case (ii) `veca , vecb and vecc` are coplanar and so `[veca vecb vecc] =0`