Given points A,B,C with their position vectors as below,
$\vec{a} = - 2024 \vec{i} + 2025 \vec{j} + 2022 \vec{k},$
$\vec{b} = 2^{2022} 3^{2023} \vec{i} + 3^{2021} 5^{2025} \vec{j} - \vec{k},$
then which of the following options is/are correct?(where O is origin)

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The point $C (\vec{c}) = \frac{2023}{2024} \vec{a} + \frac{1}{4048} \vec{b}$ lies inside of triangle formed by O, A, B as vertices.

The point $C (\vec{c}) = \frac{2024}{2025} \vec{a} + \frac{3}{2025} \vec{b}$ lies outside of triangle formed by O, A, B as vertices, but lies inside of $∠ A O B$

The point $C (\vec{c}) = \frac{- 2}{x^{2} + 1} \vec{a} + \frac{x^{2} - 1}{x^{2} + 1} \vec{b}$ lies outside of triangle formed by O, A, B as vertices, but lies inside of $∠ O A B$ $\forall x \in R$

The point $C (\vec{c}) = \frac{2}{x^{2} + 1} \vec{a} - \frac{x^{2}}{x^{2} + 1} \vec{b}$ lies outside of triangle formed by O, A, B as vertices, but lies inside of $∠ O B A$ $\forall x \in R$