Question

Show that the lines$\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}$ and $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ are perpendicular to each other.

Answer 1

The equations of the given lines are $\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}$ and $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$

The direction ratios of the given lines are 7, -5, 1 and 1, 2, 3 respectively.

Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are perpendicular to each other, if a1a2+b1b2+c1c2=0

∴7×1+(-5)×2+1×3
=7-10+3
=0

Therefore, the given lines are perpendicular to each other.