Page 72 - Math SL HB Sem 2

Koiej N{AR*A. Seremban lv{athematics IB High Level
Core : Vectors

Lines In Space
A line in space is a straight Line which continues indefinitely in both directions and
contains a continuous infrnite set ofpoints.
r

-l e*

I
A

o
y z) is a point which is free to move on a line containing a fixed point
Suppose that R(x , ,
A(xr, yr, zr) . If v: ai+ bj + ck is a direction vector of the line, it is clear that a line
consists precisely ofthose poins for which the vector AR is parallel to v, that is
--)
AR : ,tv for some scalar L (*scalar can be anything Le a,p,L,k,t or others)
-+ --)
OR-OA:2v
--) --'
OR: OA + 2u
or r :a* ly (1) vector equation

Summary:
If a straight line passes *rough A1x1,71, z1) and parallel to ai + bj + ck ,

. Its vector equation is r : (x1i +y1j + z1k) + r (ai + bj + ck)

\,