Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors, no two of which are collinear. If the vector \(\vec{a}+2\vec{b}\) is collinear with \(\vec{c}\) and \(\vec{b}+3\vec{c}\) is collinear with \(\vec{a}\), then \(\vec{a} + 2\vec{b}+6\vec{c}\) is equal to

• A. \(\lambda \vec{a}\)
• B. \(\lambda \vec{b}\)
• C. \(\lambda \vec{c}\)
• D. \(\vec{0}\)