If `vecaxxvecb=vecbxxvecc!=vec0,` then prove that `veca+vecc=tvecb`, where t is a scalar.

If vecaxxvecb=vecc,vecb xx vecc=veca, where vecc != vec0, then

If veca.vecb=0 and vecaxxvecb=0 prove that veca=vec0 or vecb=vec0 .

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

Prove that vecA.(vecAxxvecB)=0

Prove that vecA.(vecAxxvecB)=0

If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non zero vectors then (A) veca,vecb and vecc can be coplanar (B) veca,vecb and vecc must be coplanar (C) veca,vecb and vecc cannot be coplanar (D) none of these

If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc), where veca,vecb,vecc are any three vectors such that veca.vecb!=0,vecb.vecc!=0 , then veca and vecc are (A) inclined at an angle pi/3 to each other (B) inclined at an angle of pi/6 to each other (C) perpendicular (D) parallel

if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 then (a) |veca|= |vecc| (b) |veca|= |vecb| (c) |vecb|=1 (d) |veca|=|vecb|= |vecc|=1

If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are coplanar vectors, then for some scalar k prove that veca+vecc = kbvecb .

If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are coplanar vectors, then for some scalar k prove that veca+vecc = kvecb .