Question: Show that lines $x-2 = \frac{y-2}{3} = z-3$ and $x-2 = \frac{y-3}{4} = \frac{z-4}{2}$ intersect and find the coordinates of the point of intersection.
i let $x-2 = \frac{y-2}{3} = z-3 = λ $ and $x-2 = \frac{y-3}{4} = \frac{z-4}{2} = μ$
Now rearrange in terms of their parameter, and equating the x and y. I got λ = μ, what does it mean? How can i find the coordinate of their intersection?
$x-2= \dfrac{y-2}{3}=z-3$, and, $x-2= \dfrac{y-3}{4}=\dfrac{z-4}{2}$, so
$\dfrac{y-2}{3} = \dfrac{y-3}{4}$, so $y=-1$ also
$z-3 = \dfrac{z-4}{2}$ so $z = 2$, then we find $x = 1$