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Find veca.(vecbxxvecc),if veca=2overset^...

Find `veca.(vecbxxvecc)`,if
`veca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k` and
`vecc=3overset^^i+overset^^j+2overset^^k`.

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Verified by Experts

We have `veca.(vecbxxvecc)`
`=|(2,1,3),(-1,2,1),(3,1,2)|=-10`
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Find [veca" " vecb" " vecc] "if "veca=overset^^i-2overset^^j+overset^^k, vecb=2overset^^i-3overset^^j+overset^^k" and "vecc =3overset^^i+overset^^j-2overset^^k

Find the volume of a parallelepiped with coterminal edges represented by vectors veca=2overset^^i+3overset^^j+4overset^^k, vecb=3overset^^i-overset^^j+2overset^^k "and" vecc=overset^^i+2overset^^j-overset^^k .

Find the volume of the following parallelo-piped whose the coterminal edges are: veca=overset^^i-2overset^^j+3overset^^k,vecb=2overset^^i+overset^^j+overset^^k"and" vecc=2overset^^i+overset^^j-overset^^k

Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2overset^^i+3overset^^j-4overset^^k and vecc=overset^i-3overset^j+5overset^^k are coplanar.

Let " "veca=overset^^i+4overset^^j+2overset^^k, vecb=3overset^^i-2overset^^j+7overset^^k"and" vecc=2overset^^i-overset^^j+4overset^^k. Find a vector vecd perpendicular to both veca"and"vecb"and"vecc.vecd=15 .

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

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

Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^i+overset^^j+2overset^^k " and " overset^^i+lambdaoverset^^j-3overset^^k are coplanar.

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

Show that the points A,B and C with position vectors oversetrarra =3overset^^i-4overset^^j-4overset^^k," " oversetrarrb= 2overset^^i-overset^^j+overset^^k " and " oversetrarrc=overset^^i-3overset^^j-5overset^^k respectively form the vertices of a right angled triangle.

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Let the vectorsveca"and"vecbbe such that |veca|=3"and"|vecb|=sqrt2/3,...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. 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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  15. If veca,vecb,veccare coplanar,prove that veca+vecb,vecb+vecc,vecc+veca...

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

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

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

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

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

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