My knowledge on vectors is minimal. Help on the math and whether my thinking is correct is very appreciated.
Let’s assume we have the following:

start(1,1,1)
vector 
direction(?,?,?)
vector 
end(?,?,?)
vector 
distance
betweenstart()
end()
Some details:

The
direction()
vector is the mouse and constantly moving so I have to calculate it first.  The
end()
vector is always betweenstart()
anddirection()
on the same line.
So to calculate end()
, I need:
 the direction between
start()
anddirection()
 then add the distance to the
start()
vector based on thedirection()
Possible solution I have in my mind
To get the direction, I need to
direction().subtract(start())
And then normalize()
the result?
But how do I add the distance based on the new unit vector?
Sorry if I got the terminology wrong. Is this book Mathematics for 3D Game Programming and Computer Graphics: Amazon.co.uk: Eric Lengyel: 8601419489978: Books the right one to better understand the math?
@JohnK your help is very appreciated!