Thread: Proving this Parametric Equation of a Line

Hi,

I`m having trouble proving these statements involving a linear equation:

In R_n, given x = a + t*(b-a) where t is an element of [0,1] prove that:

Selecting any two values t1 and t2, the vectors connecting the two points are parallel.

The Line segment does not extend beyond points a and b.

Thanks a lot!

Originally Posted by AKTilted

proving these statements involving a linear equation:
In R_n, given x = a + t*(b-a) where t is an element of [0,1] prove that:
Selecting any two values t1 and t2, the vectors connecting the two points are parallel.
The Line segment does not extend beyond points a and b.

Does this make sense to you?
If then is a multiple of .

If so then note that
Likewise

So?

P.S. As stated it may be false if