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Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb...

Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` be three non-zero vectors such that `vecc` is a unit vector perpendicular to both `veca and vecb`. If the angle between `veca and vecb is pi//6` then the value of `|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|"is"`

A

`0`

B

`1`

C

`1/4|veca|^(2)|vecb|^(2)`

D

`3/4|veca|^(2)|vecb|^(2)`

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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. Let veca,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

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  2. If vecA, vecB and vecC are three non - coplanar vectors, then (vecA.ve...

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  3. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

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  4. If non-zero vectors veca and vecb are perpendicular to each ot...

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  5. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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  6. If veca,vecb, vecc and vecp,vecq,vecr are reciprocal system of vectors...

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  7. vecaxx(vecaxx(vecaxxvecb)) equals

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  8. If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vec...

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  9. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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  10. Let a,b and c be distinct non-negative numbers. If the vectors ahati +...

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  11. If vecaxxvecb=vecc and vecbxxvecc=veca, show that veca,vecb,vecc are o...

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  12. Let veca , vecb and vecc be vectors forming right- hand triad . Let ve...

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  13. vecrxxveca=vecbxxveca,vecrxxvecb=vecaxxvecb,vecanevec0,vecbnevec0,veca...

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  14. The vector veca coplanar with the vectors hati and hatj perendicular t...

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  15. If the vectors veca and vecb are mutually perpendicular, then veca xx ...

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  16. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  17. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  18. If the vectors (sec^(2)A)hati+hatj+hatk, hati+(sec^(2)B)hatj+hatk,hati...

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  19. x and y are two mutually perpendicular unit vector, if the vectors aha...

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  20. The three concurrent edges of a parallelopiped represent the vectors ...

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