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If hata,hatb and hatc are three unit vec...

If `hata,hatb and hatc` are three unit vectors inclined to each other at an angle `theta`. The maximum value of `theta` is

A

`pi/3`

B

`pi/2`

C

`(2pi)/3`

D

`(5pi)/6`

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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

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  3. If hata,hatb and hatc are three unit vectors inclined to each other at...

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  4. Let the pair of vector veca,vecb and vecc,veccd each determine a plane...

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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 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

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  8. The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k ...

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  9. The value of x for which the angle between veca = 2x^(2) hati + 4x h...

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  10. If vectors veca and vecb are two adjacent sides of parallelograsm then...

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  11. A parallelogram is constructed on 3veca+vecb and veca-4vecb, where |ve...

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  12. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

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  13. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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

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  15. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

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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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  17. G is the centroid of triangle ABC and A1 and B1 are the midpoints of s...

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  18. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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  19. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

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  20. If veca and vecb are any two vectors of magnitude 2 and 3 respective...

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