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

Options

A. `sqrt13`
B. `2sqrt13`
C. `6sqrt13`
D. `10sqrt13`

Answer

c

Explanation

`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`