Find `|oversetrarra|"and" |oversetrarrb| if
` `(oversetrarra+oversetrarrb).(oversetrarra-oversetrarrb) =8 " and " |oversetrarra| = 8 |oversetrarrb|`

Show that (oversetrarra-oversetrarrb) xx(oversetrarra+oversetrarrb)=2(oversetrarraxxoversetrarrb)

Given |oversetrarra| =10,|oversetrarrb| =2" and "oversetrarra.oversetrarrb=12" find "|oversetrarraxxoversetrarrb|.

If oversetrarra is a unit vector and (oversetrarrx-oversetrarra) .(oversetrarrx +oversetrarra) =15, then find |oversetrarrx| .

Find |oversetrarra-oversetrarrb| if two vectors " " oversetrarra" and "oversetrarrb are such that |oversetrarra|=2, " " |oversetrarrb|=3" and "oversetrarra.oversetrarrb=4

Show that ""|oversetrarra|oversetrarrb +|oversetrarrb| oversetrarra"" is perpendicular to |oversetrarra|oversetrarrb-|oversetrarrb| oversetrarra, for any two non-zero vectors.

If oversetrarra +5 oversetrarrb=oversetrarrc"and"oversetrarra-7oversetrarrb=2oversetrarrc, then show that oversetrarra has same direction as oversetrarrc and opposite direction to oversetrarrb .

Consider the vectors oversetrarra=2overset^^i+3overset^^j+moverset^^k " and " oversetrarrb=3overset^^i +2 overset^^j -3overset^^k Find the value of m for which oversetrarra "and"oversetrarrb are perpendicular. In such a case verify that (oversetrarra+oversetrarrb)^2=|oversetrarra""^2|+|oversetrarrb""^2|

Find a unit vector perpendicular to each of the vectors oversetrarra+oversetrarrb" and " oversetrarra-oversetrarrb where oversetrarra =3overset^^i+2overset^^j+2overset^^k" and "oversetrarrb=overset^^i+2overset^^j-2overset^^k .

Find |oversetrarraxxoversetrarrb|" if " oversetrarra=overset^^i-7overset^j+7overset^^k and oversetrarrb=3overset^^i-2overset^^j +2overset^^k.