Describe a how you use vectors to determine if three given points are collinear ?
Test your method using the set of points p(-3,1) q(2,4) r(5,6)
Hello,
Two vectors $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ are colinear if there exists a real number $\displaystyle \lambda$ different from 0 such as $\displaystyle \vec{a}=\lambda \vec{b}$
If three points are colinear, then two vectors joining two of them are colinear.. This means that if there are A, B and C three different points, and that you want to show that they are colinear, you just have to prove that $\displaystyle \vec{AB}$ and $\displaystyle \vec{AC}$, for example, are colinear.
You can see that $\displaystyle \overrightarrow {pq} = \left\langle {5,3} \right\rangle \,\& \,\overrightarrow {pr} = \left\langle {8,5} \right\rangle $
Are those vectors multiples of each other (i.e. parallel)?
If yes then you can say that they are collinear in $\displaystyle \Re^2$.
Both are in use. About 10 years or more ago there was in fact a bitter argument afoot about the use of the so-called ‘blackboard font’. There were some very prominent names in the editorial circles who were against. I have forgotten the details. For me I don’t really care. When I am just quickly typing it is easier to use \Re rather than \mathbb{R}. I tend use the latter if I am also using MathType.