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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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  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 t...

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  6. If veca=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 vecu and vecv be unit vectors such that vecu xx vecv + vecu = vecw...

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  10. The volume of the tetrahedron whose vertices are the points with posit...

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  11. Given that vecu = hati + 2hatj + 3hatk , vecv = 2hati + hatk + 4hatk ,...

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  12. Let a three- dimensional vector vecV satissgy the condition , 2vecV + ...

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

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  14. Let vec O A- vec a , hat 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 acrting on...

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  16. From a point O inside a triangle ABC, perpendiculars OD, OE and OF are...

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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. A , B , Ca n dD are any four points in the space, then prove that |...

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

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