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If veca ,vecb and vecc are three mutuall...

If `veca ,vecb and vecc` are three mutually orthogonal unit vectors , then the triple product `[veca+vecb+veccveca+vecb vecb +vecc]` equals

A

0

B

1 or -1

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
b
Here `[veca vecb vecb] = +- 1`
`[veca +vecb +vecc veca +vecb vecb +vecc]`
` (veca + vecb +vecc) xx (veca +vecb) . (vecb +vecc)`
` vecc xx (veca +vecb) . (vecb +vecc)`
` (vecc xx veca +vecc xx vecb). (vecb +vecc)`
` = vecc xx veca .vecb = [veca vecb vecc] +- 1`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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

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  4. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

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

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

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

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

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  9. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

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  10. Value of [vec a xx vec b,vec a xx vecc,vec d] is always equal to

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  11. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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

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

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

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  15. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

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  16. If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec...

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  17. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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  18. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  19. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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  20. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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