Answer to Question #114684 in Analytic Geometry for Grant Spaans

Question

8.1 Let L1 and L2 be lines defined by
x = w0 + su; s 2 R
and y = w1 + tv; t 2 R; respectively:
Show that L1and L2 are parallel if and only if u = kv for some k 2 R:

Answer 1

Let L1 and L2 be lines defined by

$x = w_0 + su; s\in R$

$y = w_1 + tv; t\in R$

Show that L1and L2 are parallel if and only if u = kv for some k $\in$ R

u & v are the direction ratios of the lines L1 & L2

for the lines to be parallel the direction ratio of one line must the scalar multiple of the other line.

so if u = kv i.e u is the multiple of v hence the line L1 & L2 are parallel to each other