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

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

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

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

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

If " " oversetrarra=2overset^^i+2overset^^j+3overset^^k," " oversetrarrb= -overset^^i+2overset^^j+overset^^k " and " oversetrarrc = 3overset^^i+overset^^j are such that oversetrarra+lambda oversetrarrb is perpendicular to oversetrarrc ,then find the value of lambda

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

If oversetrarra"and"oversetrarrb are two collinear vectors, then which of the following are incorrect: a) oversetrarrb =oversetrarra lambdascalar"lambda b) oversetrarra = +-oversetrarrb c)The respective components of oversetrarra "and "oversetrarrb are proportional d)Both oversetrarra"and" oversetrarrb have same direction, but different magnitude.

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

Consider two vectors oversetrarra "and" oversetrarrb so that |oversetrarra|=2,|oversetrarrb|=5 "and"|oversetrarraxxoversetrarrb|=8. Suppose the angle between a and b is acute. Prove that oversetrarra.oversetrarrb=6

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 .