The question is find the vector equation for the line passing through the point P= (4,7,8) and parallel to the line:
x = 8 + 8t
y = -7 + 8t
z = 6 – 2t
I have a feeling that I should take the distance between the two lines but for example the "t" in the 8 + 8t part is confusing me.
The format is like this:
[0,0,0] + t[0,0,0]
I think part of the answer is:
[4,7,8] but not sure what the t part is
Best Answer
The given line
$$x = 8 + 8t \quad y = -7 + 8t \quad z = 6 - 2t\implies (8,-7,6)+t\cdot (8,8,-2)$$
has direction vector $$v=(8,8,-2)$$
Then the line passing through $P$ and parallel to the given line is
$$P+t\cdot v=(4,7,8)+t\cdot (8,8,-2)$$