3D Vector Stuff

Hello sci/math.

I just stared Calc III at uni and am stuck on one of my homework problems.  I think I have worked it out correctly, however, like most math books, the even answers are missing from the back of the book. The most frustrating part is that they are excluded from the solutions manual which I shelled out extra money for... but that's besides the point..

The problem is as follows:

Let P = (2, 1, -1) and Q = (4, 7, 7). Find the coordinates of the point on PQ lying two thirds the way from P to Q.

First I set up the equation of my line...
L(t) = (1-t)<2, 1, -1> + t<4, 7, 7>
L(t) = <2-2t, 1-t, -1+t> + <4t, 7t, 7t>
L(t) = <2+2t, 1+6t, -1+8t>
Secondly, set t = 2/3
L(2/3) = <2+2(2/3), 1+6(2/3), -1+8(2/3)>
which gives me...
<10/3, 5, 13/3>

I basically set this up the same way as finding the midpoint between them, but replaced 1/2 with 2/3...

Was I correct in doing this this way?

Thanks in advance. (Your reward is on /s/.)

nevermind, found a copy of the sol. manual w/ the evens!