Given that `vecp=veca+vecb and vecq=veca-vecb and |veca|=|vecb|, show that vecp.veca=0`

If |veca+vecb|=|veca-vecb| show that veca_|_vecb .

Let veca and vecb be two vectors of equal magnitude 5 units. Let vecp,vecq be vectors such that vecp=veca-vecb and vecq=veca+vecb . If |vecp xx vecq|=2{lambda-(veca.vecb)^(2)}^(1/2) , then value of lambda is

Let veca, vecb, vecc be three non-zero non coplanar vectors and vecp, vecq and vecr be three vectors given by vecp=veca+vecb-2vecc, vecq=3veca-2vecb+vecc and vecr=veca-4vcb+2vecc If the volume of the parallelopiped determined by veca, vecb and vecc is V_(1) and that of the parallelopiped determined by veca, vecq and vecr is V_(2) , then V_(2):V_(1)=

given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

Let veca, vecb, vecc be three non - zero, non - coplanar vectors and vecp, vecq, vecr be three vectors given by vecp=veca+2vecb-2vecc, vecq=3veca+vecb -3vecc and vecr=veca-4vecb+4vecc . If the volume of parallelepiped determined by veca, vecb and vecc is v_(1) cubic units and volume of tetrahedron determined by vecp, vecq and vecr is v_(2) cubic units, then (v_(1))/(v_(2)) is equal to

If the two adjacent sides of two rectangles are reprresented by vectors vecp=5veca-3vecb, vecq=-veca-2vecband vecr=-4 veca-vecb,vecs=-veca+vecb , respectively, then the angle between the vectors vecx=1/3(vecp+vecr+vecs) and vecy=1/5(vecr+vecs) is

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,vecc be non coplanar vectors and vecp=(vecbxxvecc)/[veca vecb vecc], vecq=(veccxxveca)/[veca vecb vecc], vecr=(vecaxxvecb)/[veca vecb vecc] then (A) vecp.veca=1 (B) vecp.veca+vecq+vecb+vecr.vecc=3 (C) vecp.veca+vecq.vecb+vecr.vecc=0 (D) none of these

If |veca + vecb| =60 |veca-vecb|=40 and |vecb| = 46 find |veca|