Angle between the lines with direction ratios a₁, b₁, c₁ and a₂, b₂, c₂ is given by

A line passing through A(x₁, y₁, z₁) and B(x₂, y₂, z₂) has direction ratios (x₁ - x₂), (y₁ - y₂), (z₁ - z₂)

Direction ratios of line joining the points A(1,2,3) and B(4,5,7)

= (4 - 1), (5 - 2), (7 - 3)

= (3,3,4)

∴ a₁ = 3, b₁ = 3, c₁ = 4

Direction ratios of line joining the points C(-4, 3, -6) and B(2,9,2)

= (2 - (-4)), (9 - 3), (2-(-6))

= (6,6,8)

∴ a₂ = 6, b₂ = 6, c₂ = 8

Now,

∴ cosθ = 1

So, θ = 0°

Hence, Angle between the lines AB and CD is 0°.