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Let ℙ1[0, 1] be the set of non-vertical lines (y = mx + b) restricted to...

Let ℙ1[0, 1] be the set of non-vertical lines (y = mx + b) restricted to [0, 1], with usual function
addition and scalar multiplication, and define the inner product:
< ? | ? > = ∫ ?? ?? 1
0 .
A) Find the length (using this inner product) of an arbitrary line y = mx + b.
B) Find the angle between L1: y = x + 2 and L2: y = 4 – x.
C) Find the distance between the above two lines.

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