Vectors · Maximum of magnitude expression

\vec a

and

\vec b

are two vectors such that

\lvert\vec a\rvert = 2

and

\lvert\vec b\rvert = 3

, then the maximum value of

3\left\lvert\left(3\vec a + 2\vec b\right)\right\rvert + 4\left\lvert\left(3\vec a - 2\vec b\right)\right\rvert

is:

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