More vector algebra

Clematis”Ville de Lyon”

A clever way to express the equation of a line is to use the parameter form.

If C is any point on the line determined by two points a and B then we may always write

C = (1-t) A + t B

where the ratio of the real numbers t/(t-1) = AC / CB. t is the parameter with values from 0 to 1.

I give a proof for this statement:

Let AC = t AB.

This equation can be translated into

C-A = t (B-A)  → C = (1 – t) A + t B.

It is also a fact that

AB = AC + CB

AC = t (AB) → AC = t(AC + CB)  → (1 -t)AC and t/(t-1) = AC/CB


Om mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics
Detta inlägg publicerades i matematik 1c, Uncategorized. Bokmärk permalänken.


Fyll i dina uppgifter nedan eller klicka på en ikon för att logga in:

Du kommenterar med ditt Logga ut /  Ändra )


Du kommenterar med ditt Twitter-konto. Logga ut /  Ändra )


Du kommenterar med ditt Facebook-konto. Logga ut /  Ändra )

Ansluter till %s