$\vec a$ and $\vec c$ are unit collinear vectors and $|\vec b|=6$, then $\vec b-3\vec c=λ\vec a$, if λ is:

–9, 3

$|\vec a|=|\vec c|=1$ and $\vec a.\vec c=±1$ [∵ $\vec a$ and $\vec c$ are collinear]

$\vec b=λ\vec a+3\vec c⇒|\vec b|^2λ^2|\vec a|^2+9|\vec c|^2+6λ\vec a.\vec c=λ^2+9+6λ\vec a.\vec c=36$

$⇒λ^2+6λ\vec a.\vec c-27=0$

$\vec a.\vec c=±1$: consider + ive sign : $λ^2+6λ-27=0⇒λ=3, -9$

consider – ive sign : $λ^2-6λ-27=0⇒λ=9, -3$