Let a, b and c be three non-zero vectors such that no two of these are collinear.

Question

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:

Accepted Answer

Let $\vec a+2\vec b=t\vec c$ and $\vec b+3\vec c=s\vec a$. Then:

$$\vec a+2\vec b+6\vec c = t\vec c+6\vec c = (t+6)\vec c=\lambda\vec c$$

Solutions · 1