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Suppose oversetrarra =a1overset^^i+a2ove...

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`

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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

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

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

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

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

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

Consider oversetrarra=overset^^i+2overset^^j-3overset^^k," " oversetrarrb=3overset^^i-overset^^j+2overset^^k " and " oversetrarrc=11 overset^^i+overset^^j : Find the unit vector in the direction of oversetrarra+ oversetrarrb

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

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

Compute the magnitude of oversetrarra =overset^^i+overset^^j+overset^^k ,vector

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Consider the vectors " "oversetrarra=2overset^^i-3overset^^j+overset...

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  2. Consider the vectorsoversetrarra=2overset^^i-3overset^^j+overset^^k" ...

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  3. Suppose oversetrarra =a1overset^^i+a2overset^^j+a3overset^^k " ".Find...

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  4. Given that A,B,C are the points(2,1,-1),(3,2,-1)and(3,1,0).Find overse...

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  5. Find the angle between two vectorsoversetrarra"and"oversetrarrb with m...

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  6. Find the angle between the vectors overset^^i-2overset^^j+3overset^^k"...

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  7. Find the projection of the vector 'hati-hatj' on the vector 'hati+hatj...

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  8. Find the projection of a vector i+3j+7k on the vector 7i-j+8k.

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  9. Show that each of the given three vectors is a unit vector :1/7(2overs...

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  10. Find |oversetrarra|"and" |oversetrarrb| if (oversetrarra+oversetrarrb...

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  11. Evaluate the product '(3 veca-5 vecb) .(2 veca+7 vecb)'

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  12. Find the magnitude of two vectors oversetrarra"and"oversetrarrb, havin...

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  13. Find '|vecx|', if for a unit vector 'veca,(vecx-veca) .(vecx+veca)=12'

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  14. If" " oversetrarra=2overset^^i+2overset^^j+3overset^^k," " oversetrarr...

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  15. Show that""|oversetrarra|oversetrarrb +|oversetrarrb| oversetrarra"" i...

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  16. If 'veca.veca=0' and 'veca. vecb=0', then what can be concluded about ...

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  17. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, fin...

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  18. If either vecotor oversetrarra=oversetrarr0 " or " oversetrarrb=overse...

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  19. If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2)re...

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  20. Show that the points A(1,2,7),B(2,6,3) "and" C(3,10,-1) are collinear.

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