If` vecA+ vecB+vecC` =0, then show that `vecA xx vecB= vecBxxvecC= vecCxx vecA` .

If vecA+vecB+vecC=0 then show that vecAxxvecB=vecBxxvecC=vecCxxvecA .

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

If vec a , vec b and vec c are such that veca xx vecb = vecc and vecb xx vec c = vec a , prove that veca , vecb and vecc are mutually perpendicular |vecb| =1 and |vecc| = |veca| .

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

If veca, vecb, vecc and vecd are distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecb-vecc)ne 0

Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb)

If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove that (vecbxx(veca xx vecb))/(vecb.vecb)=vecq

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

If veca xx vecb + vecb xx vecc + vecc xx veca = 0 . Show that the vectors veca, vecb, vecc are coplanar.

If the three vectors veca,vecb,vecc are such that veca+vecb+vecc=vec0" and " |veca|=3,|vecb|=4,|vecc|=5 , then show that veca*vecb+vecb*vecc+vecc*veca=-25 .