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

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

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

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

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

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 .

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

Suppose oversetrarra =a_1overset^^i+a_2overset^^j+a_3overset^^k " " .Find oversetrarra.overset^^i," "oversetrarra.overset^^j" and " oversetrarra.overset^^k. Hence,prove that oversetrarra =(oversetrarra.overset^^i)overset^^i+(oversetrarra.overset^^j)overset^^j+(oversetrarra.overset^^k)overset^^k

Given that oversetrarra.oversetrarrb=0"and"oversetrarraxxoversetrarrb=oversetrarr0 .What can you conclude about the vectors oversetrarra" and "oversetrarrb.