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If vec aa n d vec b are any two vectors...

If ` vec aa n d vec b` are any two vectors of magnitudes 2 and 3, respectively, such that `|2( vec axx vec b)|+|3( vec adot vec b)|=k ,` then the maximum value of `k` is a.`sqrt(13)` b. `2sqrt(13)` c. `6sqrt(13)` d. `10sqrt(13)`

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

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  3. If vec aa n d vec b are any two vectors of magnitudes 2 and 3, resp...

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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 vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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

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  8. if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta)dot( vecal...

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  9. The position vectors of the points P,Q,R,S are hati+hatj+hatk,2hati+5h...

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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 vec ra n d vec s are non-zero constant vectors and the scalar b...

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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 ,Ba n dC of a triangle are t...

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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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