Solving vector equations

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If I know that the intersection of the two lines
$r$ vector = $x(\frac a{|a|}| + \frac b{|b|})$ and
$r$ vector = $2b + y(c - b)$
Is a point with with position vector $Z(\frac a{|a|} + \frac b{|b|})$ then what is Z?

A) the AM between |b| and |a|
B) the GM between |b| and |c|
C). The HM between |b| and |c|
D) |b| + |c|

What is the explanation?