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

$3\vec a-2\vec b$ $2\vec a-3\vec b$ $3\vec b-2\vec a$ None of these

$2\vec a-3\vec b$

$\vec d=6\hat i+12\hat j=2\vec a-3\vec b$