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Prove that [ veca+vecb vecb+vecc v...

Prove that `[ veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]`

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Hence, show that veca.vecb+vecb.vecc+vecc.veca=(-3)/2 if veca+vecb+vecc=0 .

Prove that (veca xx vecb)^2=|(veca.veca,veca.vecb),(veca.vecb,vecb.vecb)| .

Show that if veca+vecb,vecb+vecc,vecc+veca are coplanar then veca,vecb,vecc are also coplanar.

veca,vecb,vecc are three non zero vectors such that vecaxxvecb=vecc,vecbxxvecc=veca .Prove that veca,vecb,vecc are mutually at right angle and |vecb|=1,|vecc|=|veca| .

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2...

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

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

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

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

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

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

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

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

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  10. Show that the four points with position vectors4overset^^i+8overset^^j...

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  11. Find x such that the four points A(3,2,1)B(4,x,5),C(4,2,-2)and D(6,5-1...

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  12. If veca,vecb,veccare coplanar,prove that veca+vecb,vecb+vecc,vecc+veca...

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  13. Find the volume of the following parallelo-piped whose the coterminal ...

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  14. Find the volume of the following parallelo-piped whose the coterminous...

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  15. Find the value of lambdaif the points. A(-1,4,-3),B(3, lamda,-5),C(-3,...

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  16. Write down a unit vector in XY plane making an angle of 30^@ with the...

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  17. Find the scalar components and magnitude of the vector joining the poi...

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  18. A girl walks 4km towards west, then she walks 3 km in a direction 30^@...

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  19. If veca=vecb+vecc,then is it true that |veca|=|vecb|+|vecc|? Justify y...

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  20. Find the value of x for which x(overset^^i+overset^^j+overset^^k) is a...

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