$\vec{a}=3 \hat{i}-5 \hat{j}$ and $\vec{b}=6 \hat{i}+3 \hat{j}$ are two vectors and $\vec{c}$ is a vector…
$\vec{a}=3 \hat{i}-5 \hat{j}$ and $\vec{b}=6 \hat{i}+3 \hat{j}$ are two vectors and $\vec{c}$ is a vector such that $\vec{c}=\vec{a} \times \vec{b}$ then
$$
|\vec{a}|:|\vec{b}|:|\vec{c}|
$$
$\sqrt{34}: \sqrt{45}: \sqrt{39}$
$\sqrt{34}: \sqrt{45}: 39$
$34: 39: 45$
$39: 35: 34$
Solution
We have $\vec{a} \times \vec{b}=39 \vec{k}=\vec{c}$
Also $|\vec{a}|=\sqrt{34},|\vec{b}|=\sqrt{45},|\vec{c}|=39 \therefore \quad|\vec{a}|:|\vec{b}|:|\vec{c}|=\sqrt{34}: \sqrt{45}: 39$