I was wondering if anyone could shine some light on the correct thought process for this problem.
The vector equation can be expressed as the following:
$$r = a + t(b - a)$$
If I want to find a point on this line, I look to $r$. In addition, I can relate each projection of $r$ in the $x, y$ and $z$ axes using:
$r_x = a_x + t(n_x)$
$r_y = a_y + t(n_y)$
$r_z = a_z + t(n_z)$
However, how can I tweak these values to satisfy them being 3 units away from A? Do I make $r_x = 3 - a_x$ for each axis? If not, why does that not work? I feel like that would be logical, but I don't know how that could get me anywhere. Would appreciate any guidance on how to express this condition asked for in the problem.