If `(atimesb)timesc=atimes(btimesc)`, where a, b and c are any three vactors such that `a*bne0, b*cne0,` then a and c are

Options

A. inclined at angle `(pi)/3` between them
B. inclined at angle of `(pi)/6` between them
C. perpendicular
D. parallel

Answer

D

Explanation

We have
`(vecaxxvecb)xxvecc=vecaxxv(vecbxxvecc)`
`hArr-{(veccxx(vecaxxvecb))}=vecaxx(vecbxxvecc)`
`hArr-{(vecc.vecb)veca-(vecc.veca)vecb}=(veca.vecc)vecb-(veca.vecb)vecc`
`hArr-(vecc.vecb)veca+(veca.vecc)vecb=(veca.vecc)vecc-(veca.vecb)vecc`
`hArr-(vecc.vecb)veca=-(veca.vecb)vecc`
`hArr-(vecc.vecb)veca=-(veca.vecb)vecc`
`hArr(vecc.vecb)veca=(veca.vecb)vecc`
`hArrveca=((veca.vecb))/((vecc.vecb))vecc`
`hArrveca=lamdavecc` where `lamda=(veca.vecb)/(vecc.vecb)`
`hArrveca` and `vecc` are parallel