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Show that (oversetrarra-oversetrarrb) x...

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`(oversetrarra-oversetrarrb) xx(oversetrarra+oversetrarrb)=2(oversetrarraxxoversetrarrb)`

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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.

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 .

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

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 .

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

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

Consider the vectors oversetrarra=overset^^i-overset^^j+overset^^k" and "oversetrarrb=2overset^^i-3overset^^j-5overset^^k : Prove that oversetrarraxxoversetrarrb= -oversetrarrbxxoversetrarra

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Find a unit vector perpendicular to each of the vectors oversetrarra+o...

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  2. Choose the correct answer from the backet. If a unit vector hata makes...

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

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  4. Find lambdaand mu if (2overset^^i+6overset^^j+27overset^^k)xx(overset^...

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  5. Given that oversetrarra.oversetrarrb=0"and"oversetrarraxxoversetrarrb=...

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  6. If either veca=vec0"or" vecb =vec0, "then"vecaxxvecb=vec0.Is the conve...

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  7. Find the area of the triangle with vertices A(1,1,2),B(2,3,5) and C(1,...

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  8. Find the area of the parallelogram whose adjacent are determined by th...

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  9. Let the vectorsveca"and"vecbbe such that |veca|=3"and"|vecb|=sqrt2/3,...

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  10. Area of a rectangle having vertices A,B,C and D with position vectors-...

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  11. Find veca.(vecbxxvecc),if veca=2overset^^i+overset^^j+3overset^^k.vecb...

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  12. Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2...

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  13. Show that the four points A,B,C and D with position cectors 4overset^^...

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  14. Prove that [ veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

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  15. Find the volume of a parallelepiped with coterminal edges represented ...

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  16. Find [veca" " vecb" " vecc] "if "veca=overset^^i-2overset^^j+overset^^...

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  17. Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2...

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  18. Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^...

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  19. Letveca=overset^^i+overset^^j+overset^^k,vecb=overset^^i "and " vecc=c...

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  20. Letveca=overset^^i+overset^^j+overset^^k,vecb=overset^^i "and " vecc=c...

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