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If veca and vecb are any two unit vector...

If `veca and vecb` are any two unit vectors, then find the greatest postive integer in the range of `(3|veca + vecb|)/2+2|veca-vecb|`

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The correct Answer is:
5
Let angle between `veca and vecb br theta`
we have ` |veca| = |vecb|=1`
Now `|veca + vecb|= 2cos theta/2 and |veca - vecb|=2 sin theta/2`
consider `F(theta) = 3 cos theta/2 + 4 sin theta/2 theta in [ 0,pi]`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Valume of parallelpiped formed by vectors veca xx vecb, vecb xx vecc a...

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  3. If veca and vecb are any two unit vectors, then find the greatest post...

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  4. Let vecu be a vector on rectangular coodinate system with sloping angl...

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  5. Find the absolute value of parameter t for which the area of the ...

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

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  7. Let veca=alphahati+2hatj- 3hatk, vecb=hati+ 2alphahatj - 2hatk and vec...

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  8. If vec x , vec y are two non-zero and non-collinear vectors satisf...

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  9. Let vec u a n d vec v be unit vectors such that vec uxx vec v+ vec u...

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  10. The volume of the tetrahedronwhose vertices are the points with positi...

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  11. Given that vec u= hat i-2 hat j+3 hat k ; vec v=2 hat i+ hat j+4 hat k...

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  12. Let a three dimensional vector vec V satisfy the condition, 2 vec ...

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  13. If veca, vecb,vecc are unit vectors such that veca.vecb = 0= veca.vecc...

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  14. Let vec O A- vec a , vec O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

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  15. Find the work done by the force F=3 hat i- hat j-2 hat k acting on a...

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  16. from a point O inside a triangle ABC, perpendiculars, OD, OE and OF ar...

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  17. A(1),A(2), …. A(n) are the vertices of a regular plane polygon with n ...

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  18. If c is a given non - zero scalar, and vecA and vecB are given non- ze...

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  19. If A, B , C ,D are any four points in space, prove that |vec(AB)xx ve...

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  20. If vectors veca, vecb and vecc are coplanar, show that |{:(veca, vecb,...

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