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If veca is parallel to vecb xx vecc, the...

If `veca` is parallel to `vecb xx vecc, then (veca xx vecb) .(veca xx vecc) ` is equal to

A

`|veca|^(2)(vecb.vecc)`

B

`|vecb|^(2)(veca .vecc)`

C

`|vecc|^(2)(veca.vecb)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
` (veca xx vecb) . (veca xx vecc) = (veca xx vecb) . Vecu, " where " vecu = vecaxx vecc`
` Rightarrow veca. (vecb xx vecu) = veca. [vecb xx (veca xx vecc)]`
`veca . [ (vecb.vecc) veca - (veca. Vecb)vec]`
`=veca . (vecb.vecc) veca ( veca. vecb =0)`
` |veca|^(2) (vecb.vecc)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

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  2. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

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  3. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

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  4. about to only mathematics

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  5. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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  6. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  7. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

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  8. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  9. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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  10. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

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  11. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

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  12. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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  13. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  14. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  15. If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  16. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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  17. Let vec aa n d vec b be mutually perpendicular unit vectors. Then f...

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  18. Let veca and vecb be unit vectors that are perpendicular to each other...

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  19. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  20. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

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