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If veca and vecb are any two vectors o...

If `veca and vecb ` are any two vectors of `magnitude` `2 and 3` respectively such that `|2(vecaxxvecb)|+|3(veca.vecb)|=k` then the maximum value of k is

A

`sqrt13`

B

`2sqrt13`

C

`6sqrt13`

D

`10sqrt13`

Text Solution

Verified by Experts

The correct Answer is:
c
`k= |2(veca xx vecv) |+ |3 (veca .vecb) |`
` = 12 sin theta + 18 cos theta`
` Rightarrow` maximum value of k = `sqrt(12^(2) + 18^(2)) = 6sqrt13`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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

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

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  4. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

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  5. If the vector product of a constant vector vec O A with a variable...

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  6. Let vecu,vecv,vecw be such that |vecu|=1,|vecv|=2,|vecw|3. If the proj...

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  7. If the two adjacent sides of two rectangles are reprresented by vector...

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  8. If vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvec...

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  9. The position vectors of points A,B and C are hati+hatj,hati + 5hatj -h...

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  10. Given three vectors eveca, vecb and vecc two of which are non-collinea...

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  11. If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3ve...

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  12. If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n...

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  13. Resolved part of vector veca and along vector vecb " is " veca1 and th...

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  14. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

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  15. If P is any arbitrary point on the circumcirlce of the equllateral ...

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  16. If vecr and vecs are non-zero constant vectors and the scalar b is cho...

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  17. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  18. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

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  19. The position vectors of the vertices A, B and C of a triangle are thre...

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  20. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

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