If `vecaxxvecb=vecc` and `vecbxxvecc=veca`, show that `veca,vecb,vecc` are orthogonal in pairs. Also show that `|vecc|=|veca| and |vecb|=1`

If vecaxxvecb=vecc and vecbxxvecc=veca then a. veca,vecb,vecc are orthogonal in pairs and |veca|=|vecc|,|vecb|=1 b. veca,vecb,vecc are not orthogonal to each other c. veca,vecb,vecc are orthogonal in pairs but |veca|!=|vecc| d. veca,vecb,vecc are orthogonal but |vecb|=1 OR If vecaxxvecb=vecc,vecbxxvecc=veca , then

veca,vecb,vecc are three vectors such that vecaxxvecb=vecc, vecbxxvecc=veca. Prove that veca,vecb,vecc are mutually at righat angles and |vecb|=1, |vecc|=|veca| .

If veca,vecb,vecc are three such that vecaxxvecb=vecc, vecbxxvecc=veca and veccxxveca=vecb , show that veca,vecb,vecc foem an orthogonal righat handed triad of unit vectors.

If veca, vecb and vecc are three non zero vectors such that veca xx vecb = vecc and vecbxx vecc = veca. Prove that veca, vecb and vecc are mutually at right angles and |vecb|=1 and |vecc| =|veca|

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vecd) is parallel to (vecb-vecc) . It is given that veca!=vecd and vecb!=vecc .

If veca,vecb,vecc are coplanar, show that veca+vecb, vecb+vecc, vecc+veca are also coplanar.

If vecax(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0 , and [(veca,vecb,vecc)]=

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

If |veca|=1,|vecb|=2,|vecc|=3and veca+vecb+vecc=0 the show that veca.vecb+vecb.vecc+vecc.veca=- 7

If (veca xx vecb) xx vecc = veca xx (vecb xx vecc) where veca, vecb and vecc are any three vectors such that veca.vecb =0, vecb.vecc=0 then veca and vecc are: