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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`.

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

Are the vectors oversetrarra =2 overset^^i -overset^^j "and"oversetrarrb =overset^^i+2overset^^j equal?

Find the angle between the vectors " " oversetrarra=overset^^i+overset^^j-overset^^k " and "oversetrarrb=overset^^i-overset^^j+overset^^k

Find the sum of the vectors oversetrarra =overset^^i-2overset^^j+overset^^k,oversetrarrb=-2overset^^i+4overset^^j+5overset^^k " and " oversetrarrc=overset^^i-6overset^^j-7overset^^k

Consider the vectors oversetrarra=2overset^^i+3overset^^j+overset^^k " and " oversetrarrb=3overset^^i +2 overset^^j -3overset^^k find oversetrarra.oversetrarrb

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

Consider the vectors " " oversetrarra=2overset^^i-3overset^^j+overset^^k" and "oversetrarrb = overset^^i+overset^^j-2overset^^k. "" Find |3 oversetrarra+oversetrarrb |

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Consider two vectors oversetrarra "and" oversetrarrb so that|overset...

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  2. Find |oversetrarraxxoversetrarrb|" if " oversetrarra=overset^^i-7overs...

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  3. Find a unit vector perpendicular to each of the vectors oversetrarra+o...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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