the lines with direction cosines 1/11, 3/11, 4/11 and 4/11, -5/11, -1…

The lines with direction cosines l₁, m₁, n₁ and l₂, m₂,n₂  are perpendicular to each other if

l₁.l₂+ m₁.m₂+ n₁.n₂ = 0

We have the lines with direction cosines 1/11, 3/11, 4/11 and 4/11, -5/11, -1/11

so  l₁.l₂+ m₁.m₂+ n₁.n2 = (1/11).(4/11) + (3/11).(-5/11) + (4/11).(-1/11)

⇒  l₁.l₂+ m₁.m₂+ n₁.n2 = (4/121) -(15/121) - (4/121)

⇒  l₁.l₂+ m₁.m₂+ n₁.n₂ = -15/121 ≠ 0

Therefore the line are non-perpendicular.