A parallelogram is constructed on $5\vec a+2\vec b$ and $\vec a-3\vec b$ where $|a| = 2\sqrt{2}$ and |b| = 3. If the angle between $\vec a$ and $\vec b$ is π/4, then the length of the longer diagonal is

$\sqrt{593}$

The vector representing one of the diagonals is $5\vec a+2\vec b+\vec a-3\vec b=6\vec a-\vec b$

Hence the length of the diagonal =$\sqrt{(6\vec a-\vec b).(6\vec a-\vec b)}$

$=\sqrt{36|\vec a|^2+|\vec b|^2-12\vec a.\vec b}=\sqrt{36×8+9-12×3×2} =15$

The other diagonal is $5\vec a+2\vec b-\vec a+3\vec b=4\vec a+5\vec b$

Its length = $\sqrt{16|\vec a|^2+25|\vec b|^2+40\vec a.\vec b}$

$=\sqrt{128+225+40×2×3}=\sqrt{593}$

Hence (B) is the correct answer.