Find the point of intersection, , of the lines and . Please help!
Yes you are right.
I made a dumb mistake of assuming t must be same.Sorry
$\displaystyle (3,5,-9) + t_2(0,2,0) = (-1,4,-8)+t_1(-4,2,1)$
$\displaystyle (3,5,-9) - (-1,4,-8) = t_1(-4,2,1) - t_2(0,2,0)$
$\displaystyle (4,1,-1) = (-4t_1,2t_1 - 2t_2,t_1)$
So $\displaystyle -4t_1 = 4 \Rightarrow t_1 = -1$
And $\displaystyle 2t_1 - 2t_2 = 1 \Rightarrow t_2 = -\frac32$
Thus $\displaystyle (-1,4,-8)+t_1(-4,2,1) = (-1,4,-8) - (-4,2,1) = (3,2,-9)$ is the right answer.