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If `vec a , vec b , and vec c` are three mutually orthogonal unit vectors, then the triple product`[ vec a+ vec b+ vec c vec a+ vec b vec b+ vec c]` equals: (a.) `0` (b.) `1 or -1` (c.) `6` (d.) 3

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 PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  3. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

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

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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 an...

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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= la...

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  9. 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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  10. Value of [ vec axx vec b , vec axx vec c , vec d] is always equal to...

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

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  12. Let vec aa n d vec b be unit vectors that are perpendicular to each ...

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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. If vecb and vecc are unit vectors, then for any arbitary vector veca,...

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

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  16. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  17. If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ...

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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 vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

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