Let \[\vec{a},\vec{b}\] and \[\vec{c}\] be three non-zero vectors such that no two of these are collinear. If the vector \[\vec{a}+2\vec{b}\] is collinear with \[\vec{c}\] and \[\vec{b}+3\vec{c}\] is collinear with \[\vec{a}\] (\[\lambda \] being some non-zero scalar) then \[\vec{a}+2\vec{b}+6\vec{c}\] equals

• A. 0
• B. \[\lambda \vec{b}\]
• C. \[\lambda \vec{c}\]
• D. \[\lambda \vec{a}\]