Answer to Question #112628 in Analytic Geometry for Mdanda Nolwazi

Question

Let L1and L2 be the line defined by
x=wo+su and w1+tv
show that L1 and L2 are parallel if and only if u=if for some k €R

Answer 1

As per the definition of a line $L1 :x=w_0 +su$ is a line which is parallel to the vector u and the point $w_0$ lies on it.

Similarly, for $L2: x=w_1+tv$ , the line is parallel to vector v and the point $w_1$ lies on it.

Thus, for the lines L1 and L2 to be parallel, their parallel vectors must be parallel to each other.

Hence, vectors u and v must be parallel.

$\implies u=kv$ for some constant $k \in R$ .

Hence Proved.