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

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

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

Let vecx, vecy and vecz be unit vectors such that vecx+vecy+vecz=veca, vecx xx(vecyxxvecz)=vecb, (vecx xxvecy)xxvecz=vecc, veca.vecx=3/2, veca.vecy=7/4 and \|veca|=2 . Find vecx,vecy,vecz in terms of veca,vecb,vecc.

If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vecb equals

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

Find the value of |vecx| if for a unit vector a (vecx-veca)(vecx+veca)=8