Show that the lines (x + 1)/3 = (y + 3)/5 = (z + 5)/7 = (z + 5)/7

Question

Show that the lines \(\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}\) and \(\frac{x-2}{1}=\frac{y-4}{3}=\frac{z-6}{5}\) intersect Also find their point of intersection.

Answer 1

Given lines are

Let two lines (i) and (ii) intersect at a point P(a, b, \(\gamma\)).

\(\Rightarrow\) \((\alpha, \beta, \gamma)\) satisfy line (i)

Again \((\alpha, \beta, \gamma)\) also lie on (ii)

Since, the value of l in both the cases is same

\(\Rightarrow\) Both lines intersect each other at a point.

\(\therefore\) Intersecting point