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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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