Given three vectors \[\vec{a}=6\hat{i}-3\hat{j},\hat{b}=2\hat{i}-6\hat{j}\] and \[\vec{c}=-2\hat{i}+21\hat{j}\] such that \[\overrightarrow{\alpha }=\vec{a}+\vec{b}+\vec{c}\]. Then the resolution of the vector \[\overrightarrow{\alpha }\] into components with respect to \[\vec{a}\] and \[\vec{b}\] is given by

• A. \[3\vec{a}-2\vec{b}\]
• B. \[3\vec{b}\]\[-\]\[2\vec{a}\]
• C. \[2\vec{a}-3\vec{b}\]
• D. \[\vec{a}-2\vec{b}\]