## Problem Statement

Are the vectors $c_{1 \text { and }} c_{2}$, constructed from vectors $a \text{ and } b$, collinear?

$a=\{-1 ; 3 ; 4\}$

$b=\{2 ;-1 ; 0\}$

$c_{1}=6 a-2 b$

$c_{2}=b-3 a$
## Solution

Vectors are collinear if there exists a number $\gamma$ such that $c_{1}=\gamma \cdot c_{2}$. That is, vectors are collinear if their coordinates are proportional.

It is not hard to notice that $c_{1}=-2(b-3 a)=-2 c_{2}$ for any $a$ and $b$.

That is, $c_{1}=-2 \cdot c_{2}$, which means the vectors $c_{1}$ and $c_{2}$ are collinear.

## Problem Kuznetsov Analytical Geometry 3-28