Evaluate :

`veca . ( vecb - vecc )`

Let |veca| = 3, |vecb| = 5, vecb.vecc= 10 , angle between vecb and vecc equal to pi/3 . If veca is perpendicular vecb xx vecc then find the value of |veca xx (vecb xx vecc)|

If veca, vecb, vecc are unit vectors such that veca. Vecb =0 = veca.vecc and the angle between vecb and vecc is pi/3 , then find the value of |veca xx vecb -veca xx vecc|

If veca, vecb and vecc are three non-zero vectors, no two of which are collinear, veca +2 vecb is collinear with vecc and vecb + 3 vecc is collinear with veca , then find the value of |veca + 2vecb + 6vecc| .

If |veca|=3, |vecb|=1, |vecc|=4 and veca + vecb + vecc= vec0 , find the value of veca.vecb+ vecb+ vecc.vecc + vecc.veca .

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc))/(vecb.(vecc xx veca)) + (vecb.(vecc xx veca))/(vecc.(veca xx vecb)) +(vecc.(vecb xx veca))/(veca. (vecb xx vecc)) is equal to:

The value of [(veca-vecb, vecb-vecc, vecc-veca)] , where |veca|=1, |vecb|=5, |vecc|=3 , is

If veca = (hati - 2hatj), vecb = (2hati - 3hatj) and vecc = (2hati + 3hatk) , find (veca + vecb + vecc) .