Show that the line `(x-1)/2=(y-2)/3=(z-3)/4a n d(x-4)/5=(y-1)/2` intersect. Find their point of intersection.

Explanation

line1: `frac{{x}-{1}}{2}=frac{{y}-{2}}{3}=frac{{z}-{3}}{4}={t}`


line 2: `frac{x-4}{5}=frac{y-1}{2}=frac{z}{1}`


`({x}, {y}, {z})=(2 {t}+1,3 {t}+2,4 {t}+3) `be a point on line1.


for this point of to be point of intersection of line1 & line 2 it must satisy line2.



`rightarrow frac{2 t+1-4}{5}=frac{3 t+2-1}{2}=frac{4 t+3}{1}`


`
Rightarrow t=-1`


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