If $\vec a = 3\hat i-5\hat j$ and $\vec b = 6\hat i +3\hat j$ are two vectors and $\vec c$ is a vector such that $\vec c = \vec a×\vec b$, then $|\vec a|:|\vec b|:|\vec c|=$

$\sqrt{34}:\sqrt{45}:39$

We have,

$\vec a=3\hat i-5\hat j, \vec b = 6\hat i +3\hat j$ and $\vec c = \vec a×\vec b$

$⇒\vec a=3\hat i-5\hat j, \vec b = 6\hat i +3\hat j$ and $\vec c = 39\hat k$

$⇒|\vec a|=\sqrt{34},|\vec b|=\sqrt{45}$ and $\vec c = 39$

$⇒|\vec a|:|\vec b|:|\vec c|=\sqrt{34}:\sqrt{45}:39$