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If hat a , hat b ,a n d hat c are three...

If ` hat a , hat b ,a n d hat c` are three unit vectors inclined to each other at angle `theta,` then the maximum value of `theta` is `pi/3` b. `pi/4` c. `(2pi)/3` d. `(5pi)/6`

A

`pi/3`

B

`pi/2`

C

`(2pi)/3`

D

`(5pi)/5`

Text Solution

Verified by Experts

The correct Answer is:
c
`(hata+hatb + hatc)^(2)ge0`
`3+2(hata.hatb+vecb.hatc+vecc.veca)ge0`
` 3 + 6 cos theta ge 0`
`cos theta ge - 1/2`
`Rightarrow theta= (2pi)/3`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  5. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

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  6. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

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  7. Vectors 3 vec a-5 vec b and 2 vec a+ vec b are mutually perpendicular....

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  8. The unit vector orthogonal to vector -hat i+ hat j+2 hat k and maki...

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  9. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

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  10. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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  11. A parallelogram is constructed on 2 vec a+ vec ba n d vec a-4 vec b...

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  12. Let vec adot vec b=0,w h e r e vec aa n d vec b are unit vectors and ...

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  13. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

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  14. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

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  15. A vector of magnitude sqrt(2) coplanar with the vector vec a= hat i+ ...

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  16. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

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