If the magnitude of the sum of two non-zero vectors is equal to magnitude of their difference, then which one of the following is correct?

What is the scalar projection of

$$a = \widehat i - 2\widehat j + \widehat k$$ on

$$b = 4\widehat i - 4\widehat j + 7\widehat k$$ ?

If $$a = \widehat i - 2\widehat j + 5\widehat k$$ and $$b = 2\widehat i + \widehat j - 3\widehat k$$, then what is $$(b - a).(3a + b)$$ equal to ?

If the position vectors of points A and B are $$3\widehat i - 2\widehat j + \widehat k$$ and $$2\widehat i + 4\widehat j - 3\widehat k$$ respectively, then what is the length of AB ?