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

Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|.

Find |veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb|

Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb| .

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

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)=

Consider a parallelogram constructed on the vectors vecA=5vecp+2vecq and vecB=vecp-3vecq . If |vecp|=2, |vecq|=5 , the angle between vecp and vecq is (pi)/(3) and the length of the smallest diagonal of the parallelogram is k units, then the value of k^(2) is equal to

Prove that (veca+3vecb)xx(veca+vecb)+(3veca-5vecb)xx(veca-vecb)=0