Lines

Wednesday, 14 March 2018

12:06 AM

In two dimensional space (notated by ), the Cartesian equation a line is often written as  ( is interchangable with )

 

Lines in parametric vector form

In , any expression of the form  for some

 

Where ,

 is the co-ordinate vector of some point on the line

 is the direction of the line

 is called the parameter

 

Different values of  correspond to different co-ordinate vectors

Properties

Two lines are parallel if their direction vectors () are scalar multiples of each other

Questions regarding lines

Does the point  lie on the line ?

1. Split each dimension into their own equation

2. Solve and verify

From        

Verify  …  …  … correct

Verify  …  …  … correct

3. Conclude

Therefore, yes, the point lies on the line

Find the equation of the lines which passes through  and