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Given |oversetrarra| =10,|oversetrarrb| ...

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

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

If either vecotor oversetrarra=oversetrarr0 " or " oversetrarrb=oversetrarr0, "then "oversetrarra.oversetrarrb=0. But the converse need not be true. Justify your answer with an example.

Consider oversetrarra=overset^^i+2overset^^j-3overset^^k," " oversetrarrb=3overset^^i-overset^^j+2overset^^k " and " oversetrarrc=11 overset^^i+overset^^j : Find oversetrarra+oversetrarrb" and "oversetrarra.oversetrarrb

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

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 .

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 .

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
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  12. Find |oversetrarraxxoversetrarrb|" if " oversetrarra=overset^^i-7overs...

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