if `veca + vecb + vecc=0`, then show that `veca xx vecb = vecb xx vecc = vecc xx veca`.

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca, vecb, vecc and vecd ar distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

If vec a,vec b , vec c are unit vectors such that veca + vec b+ vecc = 0 and lambda = veca.vecb + vecb.vecc+vecc.veca and d = veca xx vecb + vecb xx vecc + vecc xx veca , then (lambda,vecd) is

Let veca vecb and vecc be three non-zero vectors such that veca + vecb + vecc = vec0 and lambda vecb xx veca xx veca + vecbxxvecc + vecc + veca = vec0 then find the value of lambda .

If |veca|=1,|vecb|=2,|vecc|=3and veca+vecb+vecc=0 the show that veca.vecb+vecb.vecc+vecc.veca=- 7

If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, veca xx vecb = veca xx vecc, a ne 0. then show that vecb = vecc.