Find a vector parametrization for the line that
satisfies the given conditions.
Passes through the point P(1,−1, 2) and is parallel to the
line r(t) = t(3i − j + k).
What I tried is to plug in P to rt
P(1,-1,2) = (3*1 -(-1)+2)= 6
Am I on the right track?
Best Answer
No, you're not on the right track. Remember that $i$, $j$, and $k$ are your standard unit vectors -- they are not variables that you can plug a point into. So don't do that.
What you should do is this:
The vector equation of a line always looks like $$r(t) = vt + b$$ where $v$ is a vector parallel to your line, $b$ is a point on your line, and $t$ is your variable. So you just need to figure out what your $v$ and $b$ vectors need to be (and because you've already used $r$ and $t$, maybe just change those to $s$ and $u$ or something).
Does that help?