The position vectors of two 1 kg particles, (A) and (B), are given by r_A =(α_1 t^2 i +α_2 t j +α_3 t k ) m and r_B =(β_1 t i +β_2 t^2 j +β_3 t k )…

The position vectors of two $\displaystyle 1$ kg particles, (A) and (B), are given by $$\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m} \text { and } \overrightarrow{\mathrm{r}}_{\mathrm{B}}=\left(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}+\beta_3 \mathrm{t} \hat{k}\right) \mathrm{m} \text {, respectively; } $$ ( $\displaystyle \alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s}, \alpha_3=2 \mathrm{~m} / \mathrm{s}, \beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{p} \mathrm{m} / \mathrm{s}$ ), where t is time, n and $\displaystyle p$ are constants. At $\displaystyle t=1 s,\left|\vec{V}_A\right|=\left|\vec{V}_B\right|$ and velocities $\displaystyle \vec{V}_A$ and $\displaystyle \vec{V}_B$ of the particles are orthogonal to each other. At $\displaystyle \mathrm{t}=1 \mathrm{~s}$, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is $\displaystyle \sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}$. The value of L is $\displaystyle \_\_\_\_$.