Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors such that \(\vec{b}\) and \(\vec{c}\) are non-colline…

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors such that \(\vec{b}\) and \(\vec{c}\) are non-collinear. If \(\vec{a}+5 \vec{b}\) is collinear with \(\vec{c}, \vec{b}+6 \vec{c}\) is collinear with \(\vec{a}\) and \(\vec{a}+\alpha \vec{b}+\beta \vec{c}=\overrightarrow{0}\),then \(\alpha+\beta\) is equal to

[JEE Main 2024, 29 Jan (Shift 1)]