Take the tour ×  So, I found the correct answer to this homework
question, but I was hoping there was an easier way to find the
same answer.  Here's the question:  Gandalf the Grey started in
the Forest of Mirkwood at a point with coordinates $(-2, 1)$ and
arrived in the Iron Hills at the point with coordinates $(-1,
6)$. If he began walking in the direction of the vector $\bf v =
5 \mathbf{I} + 1 \mathbf{J}$ and changes direction only once,
when he turns at a right angle, what are the coordinates of the
point where he makes the turn.  The answer is $((-1/13),
(18/13))$.  Now, I know that the dot product of two
perpendicular vectors is $0$, and the sum of the two
intermediate vectors must equal $\langle 1, 5\rangle$. Also, the
tutor solved the problem by using a vector-line formula which
had a point, then a vector multiplied by a scalar. I'm looking
for the easiest and most intuitive way to solved this problem.
Any help is greatly appreciated! I'll respond as quickly as I
can.  share|improve this question ad