Question

Determine if the two lines $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z}{-1}$ and $\frac{x-4}{3}=\frac{y-1}{-2}=\frac{z-1}{1}$ are coplanar.

Answer 1

Direction ratios = $<2,4,-1>$ and $<3,-2,1>$

using Co-planar properties and solving the matrices,we get

$3(4-2)+2(2+3)+1(-4-12)$

$6+10-16$

$⟹0$

As the result is 0.Hence, the lines are co-planar.