Question #114684
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:
1
Expert's answer
2020-05-12T18:35:23-0400

Let L1 and L2 be lines defined by

x=w0+su;sRx = w_0 + su; s\in R

y=w1+tv;tRy = 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


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