Consider the following three points in $R^3$ : $P(−1, 1, 0), Q(1, 5, 6), R(3, −1, 4)$
Find the values of $x ∈ R$ for which $PR + x QR$ is perpendicular to $PR$.
I was thinking that equating the dot product of those 2 vectors to $0$ might give the values. But this only gives one x value ($x=-3$) and I presume that there are more. Thoughts?