Solve the following simultaneous equation for vectors `vecx and vecy, if vecx+vecy=veca, vecx xxvecy=vecb, vecx.veca=1`

Sholve the simultasneous vector equations for vecx and vecy: vecx+veccxxvecy=veca and vecy+veccxxvecx=vecb, vecc!=0

Two vectors vecA and vecB are such that vecA+vecB=vecA-vecB . Then

For any two vectors veca and vecb prove that |veca.vecb|<=|veca||vecb|

Vectors vecA and vecB satisfying the vector equation vecA+ vecB = veca, vecA xx vecB =vecb and vecA.veca=1 . where veca and vecb are given vectosrs, are

The points with position vectors vecx + vecy, vecx-vecy and vecx +λ vecy are collinear for all real values of λ.

If the vectors veca and vecb are perpendicular to each other then a vector vecv in terms of veca and vecb satisfying the equations vecv.veca=0, vecv.vecb=1 and [(vecv, veca, vecb)]=1 is

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of (vecaxxveca\')+(vecbxxvecb\')+(veccxxvecc\') is (A) veca+vecb+vecc (B) veca\'+vecb\'+vecc\' (C) 0 (D) none of these

If veca vecb are non zero and non collinear vectors, then [(veca, vecb, veci)]hati+[(veca, vecb, vecj)]hatj+[(veca, vecb, veck)]hatk is equal to

If veca and vecb are two non collinear vectors and vecu = veca-(veca.vecb).vecb and vecv=veca x vecb then vecv is

Vectors vecx,vecy,vecz each of magnitude sqrt(2) make angles of 60^0 with each other. If vecx xx (vecyxxvecz) = veca, vecy xx (veczxxvecx) = vecb and vecx xx vecy = vecc . Find vecx, vecy, vecz in terms of veca, vecb, vecc .