If ` vec p , vec q , vec r` denote vector ` vec bxx vec c , vec cxx vec a , vec axx vec b` , respectively, show that ` vec a` is parallel to ` vec qxx vec r , vec b` is parallel ` vec rxx vec p , vec c` is parallel to ` vec pxx vec qdot`

Explanation

Here `vecP = vecb xx vecc,vecq =vecc xx veca, vecc veca, vecr = veca xx vecb `
now ` vecaxx (vecq xx vecr) = (veca .vecr) vecq- (veca .vecq) vecr`
` { veca . (veca xx vecb)} vecq - {vecb . (veca xx vecb)} vecq`
`= (0) vecq - (0) vecr = vec0`
Therefore, `vecb` is parallel to `vecr xx vecp`
Again `vecb xx (vecr xx vecp) = (vecb.vecp) = (vecb =.vecp) vecr - (vecb .vecr) vecp`
`= { veca. (veca xx vecc )} vecq - { vecb . (veca xx vecb)} vecp`
`(0) vecr - (0) vecp = vec0`
Therefore, is parallel to ` vecq xx vecp`
Also `vecc xx (vecp xxvecq) ]= (vecc. vecq)vecp - (vecc. vecp) vecq`
`= {vecc . (vecc xx veca)} vecp - {vecc. (vecb xx vecc)} vecq`
`= (0) vecr- (0) vecq =vec0`
Therefore, `vecc` is parallel to `vecp xx vecq`.