Question 10 [10 points]
Let L be the line with parametric equations
$$ x = −6−3t $$
$$ y = 6+3t $$
$$ z = −8+2t $$
Find the vector equation for a line that passes through the point P=(−1, 2, 3) and intersects L at a point that is distance 2 from the point Q=(−6, 6, −8). Note that there are two possible correct answers.
If anyone already has a similar question up, even just pointing me in the right direction would help a lot!
Best Answer
Hint:
Note the point $Q$ is on $L$, so you just need to find the point $P'$ on $L$ s.t. $|P'Q|=2$, which means you just need to find corresponding $t$. There are two $t$ satisfying the requirement.
After you get the points $P'$, just connect it with $P$ by a line.